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Simplifying x2 + 5x + 7 = -1x2 + -3x + 10 Reorder the terms: 7 + 5x + x2 = -1x2 + -3x + 10 Reorder the terms: 7 + 5x + x2 = 10 + -3x + -1x2 Solving 7 + 5x + x2 = 10 + -3x + -1x2 Solving for variable 'x'. Reorder the terms: 7 + -10 + 5x + 3x + x2 + x2 = 10 + -3x + -1x2 + -10 + 3x + x2 Combine like terms: 7 + -10 = -3 -3 + 5x + 3x + x2 + x2 = 10 + -3x + -1x2 + -10 + 3x + x2 Combine like terms: 5x + 3x = 8x -3 + 8x + x2 + x2 = 10 + -3x + -1x2 + -10 + 3x + x2 Combine like terms: x2 + x2 = 2x2 -3 + 8x + 2x2 = 10 + -3x + -1x2 + -10 + 3x + x2 Reorder the terms: -3 + 8x + 2x2 = 10 + -10 + -3x + 3x + -1x2 + x2 Combine like terms: 10 + -10 = 0 -3 + 8x + 2x2 = 0 + -3x + 3x + -1x2 + x2 -3 + 8x + 2x2 = -3x + 3x + -1x2 + x2 Combine like terms: -3x + 3x = 0 -3 + 8x + 2x2 = 0 + -1x2 + x2 -3 + 8x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -3 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 4x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 4x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 4x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 4x + x2 = 0 + 1.5 4x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 4x + x2 = 1.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.5 + 4 Reorder the terms: 4 + 4x + x2 = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 4 + 4x + x2 = 5.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + 2) equal to 2.34520788 and -2.34520788.Subproblem 1
x + 2 = 2.34520788 Simplifying x + 2 = 2.34520788 Reorder the terms: 2 + x = 2.34520788 Solving 2 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.34520788 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.34520788 + -2 x = 2.34520788 + -2 Combine like terms: 2.34520788 + -2 = 0.34520788 x = 0.34520788 Simplifying x = 0.34520788Subproblem 2
x + 2 = -2.34520788 Simplifying x + 2 = -2.34520788 Reorder the terms: 2 + x = -2.34520788 Solving 2 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.34520788 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.34520788 + -2 x = -2.34520788 + -2 Combine like terms: -2.34520788 + -2 = -4.34520788 x = -4.34520788 Simplifying x = -4.34520788Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34520788, -4.34520788}
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