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Simplifying 9x + -7 = -2x2 + 13 Reorder the terms: -7 + 9x = -2x2 + 13 Reorder the terms: -7 + 9x = 13 + -2x2 Solving -7 + 9x = 13 + -2x2 Solving for variable 'x'. Reorder the terms: -7 + -13 + 9x + 2x2 = 13 + -2x2 + -13 + 2x2 Combine like terms: -7 + -13 = -20 -20 + 9x + 2x2 = 13 + -2x2 + -13 + 2x2 Reorder the terms: -20 + 9x + 2x2 = 13 + -13 + -2x2 + 2x2 Combine like terms: 13 + -13 = 0 -20 + 9x + 2x2 = 0 + -2x2 + 2x2 -20 + 9x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -20 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + 4.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 4.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 4.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4.5x + x2 = 0 + 10 4.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 4.5x + x2 = 10 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 10 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 10 + 5.0625 Combine like terms: 10 + 5.0625 = 15.0625 5.0625 + 4.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + 2.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + 2.25 = 3.881043674 Simplifying x + 2.25 = 3.881043674 Reorder the terms: 2.25 + x = 3.881043674 Solving 2.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.881043674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.881043674 + -2.25 x = 3.881043674 + -2.25 Combine like terms: 3.881043674 + -2.25 = 1.631043674 x = 1.631043674 Simplifying x = 1.631043674Subproblem 2
x + 2.25 = -3.881043674 Simplifying x + 2.25 = -3.881043674 Reorder the terms: 2.25 + x = -3.881043674 Solving 2.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.881043674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.881043674 + -2.25 x = -3.881043674 + -2.25 Combine like terms: -3.881043674 + -2.25 = -6.131043674 x = -6.131043674 Simplifying x = -6.131043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.631043674, -6.131043674}
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