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Simplifying 137 = 7x + -5x[-2x + 10] Reorder the terms: 137 = 7x + -5x[10 + -2x] 137 = 7x + [10 * -5x + -2x * -5x] 137 = 7x + [-50x + 10x2] Combine like terms: 7x + -50x = -43x 137 = -43x + 10x2 Solving 137 = -43x + 10x2 Solving for variable 'x'. Reorder the terms: 137 + 43x + -10x2 = -43x + 43x + 10x2 + -10x2 Combine like terms: -43x + 43x = 0 137 + 43x + -10x2 = 0 + 10x2 + -10x2 137 + 43x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 137 + 43x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -13.7 + -4.3x + x2 = 0 Move the constant term to the right: Add '13.7' to each side of the equation. -13.7 + -4.3x + 13.7 + x2 = 0 + 13.7 Reorder the terms: -13.7 + 13.7 + -4.3x + x2 = 0 + 13.7 Combine like terms: -13.7 + 13.7 = 0.0 0.0 + -4.3x + x2 = 0 + 13.7 -4.3x + x2 = 0 + 13.7 Combine like terms: 0 + 13.7 = 13.7 -4.3x + x2 = 13.7 The x term is -4.3x. Take half its coefficient (-2.15). Square it (4.6225) and add it to both sides. Add '4.6225' to each side of the equation. -4.3x + 4.6225 + x2 = 13.7 + 4.6225 Reorder the terms: 4.6225 + -4.3x + x2 = 13.7 + 4.6225 Combine like terms: 13.7 + 4.6225 = 18.3225 4.6225 + -4.3x + x2 = 18.3225 Factor a perfect square on the left side: (x + -2.15)(x + -2.15) = 18.3225 Calculate the square root of the right side: 4.280478945 Break this problem into two subproblems by setting (x + -2.15) equal to 4.280478945 and -4.280478945.Subproblem 1
x + -2.15 = 4.280478945 Simplifying x + -2.15 = 4.280478945 Reorder the terms: -2.15 + x = 4.280478945 Solving -2.15 + x = 4.280478945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15' to each side of the equation. -2.15 + 2.15 + x = 4.280478945 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = 4.280478945 + 2.15 x = 4.280478945 + 2.15 Combine like terms: 4.280478945 + 2.15 = 6.430478945 x = 6.430478945 Simplifying x = 6.430478945Subproblem 2
x + -2.15 = -4.280478945 Simplifying x + -2.15 = -4.280478945 Reorder the terms: -2.15 + x = -4.280478945 Solving -2.15 + x = -4.280478945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15' to each side of the equation. -2.15 + 2.15 + x = -4.280478945 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = -4.280478945 + 2.15 x = -4.280478945 + 2.15 Combine like terms: -4.280478945 + 2.15 = -2.130478945 x = -2.130478945 Simplifying x = -2.130478945Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.430478945, -2.130478945}
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