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Simplifying 7x2 + -7x + -114 = 0 Reorder the terms: -114 + -7x + 7x2 = 0 Solving -114 + -7x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -16.28571429 + -1x + x2 = 0 Move the constant term to the right: Add '16.28571429' to each side of the equation. -16.28571429 + -1x + 16.28571429 + x2 = 0 + 16.28571429 Reorder the terms: -16.28571429 + 16.28571429 + -1x + x2 = 0 + 16.28571429 Combine like terms: -16.28571429 + 16.28571429 = 0.00000000 0.00000000 + -1x + x2 = 0 + 16.28571429 -1x + x2 = 0 + 16.28571429 Combine like terms: 0 + 16.28571429 = 16.28571429 -1x + x2 = 16.28571429 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 16.28571429 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 16.28571429 + 0.25 Combine like terms: 16.28571429 + 0.25 = 16.53571429 0.25 + -1x + x2 = 16.53571429 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 16.53571429 Calculate the square root of the right side: 4.066412951 Break this problem into two subproblems by setting (x + -0.5) equal to 4.066412951 and -4.066412951.Subproblem 1
x + -0.5 = 4.066412951 Simplifying x + -0.5 = 4.066412951 Reorder the terms: -0.5 + x = 4.066412951 Solving -0.5 + x = 4.066412951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.066412951 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.066412951 + 0.5 x = 4.066412951 + 0.5 Combine like terms: 4.066412951 + 0.5 = 4.566412951 x = 4.566412951 Simplifying x = 4.566412951Subproblem 2
x + -0.5 = -4.066412951 Simplifying x + -0.5 = -4.066412951 Reorder the terms: -0.5 + x = -4.066412951 Solving -0.5 + x = -4.066412951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.066412951 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.066412951 + 0.5 x = -4.066412951 + 0.5 Combine like terms: -4.066412951 + 0.5 = -3.566412951 x = -3.566412951 Simplifying x = -3.566412951Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.566412951, -3.566412951}
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