Solve the equation 2, x, squared, minus, 12, x, plus, 23, equals, x, squared2x 2 −12x+23=x 2 to the nearest tenth.
Question
Solve the equation 2, x, squared, minus, 12, x, plus, 23, equals, x, squared2x 2 −12x+23=x 2 to the nearest tenth.
Solution
The equation you provided seems to be a bit unclear. However, if you're asking to solve the quadratic equation 2x^2 - 12x + 23 = x^2, here are the steps:
Step 1: Simplify the equation by subtracting x^2 from both sides to get x^2 - 12x + 23 = 0.
Step 2: Identify the coefficients a, b, and c in the standard form of a quadratic equation ax^2 + bx + c = 0. Here, a = 1, b = -12, and c = 23.
Step 3: Use the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a) to solve for x.
Step 4: Substitute the values of a, b, and c into the formula.
x = [12 ± sqrt((-12)^2 - 4123)] / (2*1) x = [12 ± sqrt(144 - 92)] / 2 x = [12 ± sqrt(52)] / 2 x = [12 ± 7.21] / 2
Step 5: Solve for the two possible values of x.
x = (12 + 7.21) / 2 = 9.6 (to the nearest tenth) x = (12 - 7.21) / 2 = 2.4 (to the nearest tenth)
So, the solutions to the equation 2x^2 - 12x + 23 = x^2 are x = 9.6 and x = 2.4.
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