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Simplifying -12x2 + 17x + 8 = 4x2 + -1x + 1 Reorder the terms: 8 + 17x + -12x2 = 4x2 + -1x + 1 Reorder the terms: 8 + 17x + -12x2 = 1 + -1x + 4x2 Solving 8 + 17x + -12x2 = 1 + -1x + 4x2 Solving for variable 'x'. Reorder the terms: 8 + -1 + 17x + x + -12x2 + -4x2 = 1 + -1x + 4x2 + -1 + x + -4x2 Combine like terms: 8 + -1 = 7 7 + 17x + x + -12x2 + -4x2 = 1 + -1x + 4x2 + -1 + x + -4x2 Combine like terms: 17x + x = 18x 7 + 18x + -12x2 + -4x2 = 1 + -1x + 4x2 + -1 + x + -4x2 Combine like terms: -12x2 + -4x2 = -16x2 7 + 18x + -16x2 = 1 + -1x + 4x2 + -1 + x + -4x2 Reorder the terms: 7 + 18x + -16x2 = 1 + -1 + -1x + x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 7 + 18x + -16x2 = 0 + -1x + x + 4x2 + -4x2 7 + 18x + -16x2 = -1x + x + 4x2 + -4x2 Combine like terms: -1x + x = 0 7 + 18x + -16x2 = 0 + 4x2 + -4x2 7 + 18x + -16x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 7 + 18x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.4375 + -1.125x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -1.125x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -1.125x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -1.125x + x2 = 0 + 0.4375 -1.125x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -1.125x + x2 = 0.4375 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 0.4375 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 0.4375 + 0.31640625 Combine like terms: 0.4375 + 0.31640625 = 0.75390625 0.31640625 + -1.125x + x2 = 0.75390625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 0.75390625 Calculate the square root of the right side: 0.868277749 Break this problem into two subproblems by setting (x + -0.5625) equal to 0.868277749 and -0.868277749.Subproblem 1
x + -0.5625 = 0.868277749 Simplifying x + -0.5625 = 0.868277749 Reorder the terms: -0.5625 + x = 0.868277749 Solving -0.5625 + x = 0.868277749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.868277749 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.868277749 + 0.5625 x = 0.868277749 + 0.5625 Combine like terms: 0.868277749 + 0.5625 = 1.430777749 x = 1.430777749 Simplifying x = 1.430777749Subproblem 2
x + -0.5625 = -0.868277749 Simplifying x + -0.5625 = -0.868277749 Reorder the terms: -0.5625 + x = -0.868277749 Solving -0.5625 + x = -0.868277749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.868277749 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.868277749 + 0.5625 x = -0.868277749 + 0.5625 Combine like terms: -0.868277749 + 0.5625 = -0.305777749 x = -0.305777749 Simplifying x = -0.305777749Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.430777749, -0.305777749}
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