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Simplifying x(3x + 5) = 270 Reorder the terms: x(5 + 3x) = 270 (5 * x + 3x * x) = 270 (5x + 3x2) = 270 Solving 5x + 3x2 = 270 Solving for variable 'x'. Reorder the terms: -270 + 5x + 3x2 = 270 + -270 Combine like terms: 270 + -270 = 0 -270 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -90 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 1.666666667x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 1.666666667x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 1.666666667x + x2 = 0 + 90 1.666666667x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 1.666666667x + x2 = 90 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 90 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 90 + 0.6944444447 Combine like terms: 90 + 0.6944444447 = 90.6944444447 0.6944444447 + 1.666666667x + x2 = 90.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 90.6944444447 Calculate the square root of the right side: 9.523363085 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 9.523363085 and -9.523363085.Subproblem 1
x + 0.8333333335 = 9.523363085 Simplifying x + 0.8333333335 = 9.523363085 Reorder the terms: 0.8333333335 + x = 9.523363085 Solving 0.8333333335 + x = 9.523363085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 9.523363085 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 9.523363085 + -0.8333333335 x = 9.523363085 + -0.8333333335 Combine like terms: 9.523363085 + -0.8333333335 = 8.6900297515 x = 8.6900297515 Simplifying x = 8.6900297515Subproblem 2
x + 0.8333333335 = -9.523363085 Simplifying x + 0.8333333335 = -9.523363085 Reorder the terms: 0.8333333335 + x = -9.523363085 Solving 0.8333333335 + x = -9.523363085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -9.523363085 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -9.523363085 + -0.8333333335 x = -9.523363085 + -0.8333333335 Combine like terms: -9.523363085 + -0.8333333335 = -10.3566964185 x = -10.3566964185 Simplifying x = -10.3566964185Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.6900297515, -10.3566964185}
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