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Simplifying 126 + -10x = 2x2 Solving 126 + -10x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 0 126 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(63 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(63 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 63 + -5x + -1x2 = 0 Solving 63 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + 5x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 5x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 5x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 5x + x2 = 0 + 63 5x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 5x + x2 = 63 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 63 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 63 + 6.25 Combine like terms: 63 + 6.25 = 69.25 6.25 + 5x + x2 = 69.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + 2.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + 2.5 = 8.321658489 Simplifying x + 2.5 = 8.321658489 Reorder the terms: 2.5 + x = 8.321658489 Solving 2.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 8.321658489 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.321658489 + -2.5 x = 8.321658489 + -2.5 Combine like terms: 8.321658489 + -2.5 = 5.821658489 x = 5.821658489 Simplifying x = 5.821658489Subproblem 2
x + 2.5 = -8.321658489 Simplifying x + 2.5 = -8.321658489 Reorder the terms: 2.5 + x = -8.321658489 Solving 2.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -8.321658489 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.321658489 + -2.5 x = -8.321658489 + -2.5 Combine like terms: -8.321658489 + -2.5 = -10.821658489 x = -10.821658489 Simplifying x = -10.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.821658489, -10.821658489}Solution
x = {5.821658489, -10.821658489}
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