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Simplifying 3x2 + -4x = 1500 Reorder the terms: -4x + 3x2 = 1500 Solving -4x + 3x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + -4x + 3x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -500 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + -1.333333333x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -1.333333333x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -1.333333333x + x2 = 0 + 500 -1.333333333x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -1.333333333x + x2 = 500 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 500 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 500 + 0.4444444442 Combine like terms: 500 + 0.4444444442 = 500.4444444442 0.4444444442 + -1.333333333x + x2 = 500.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 500.4444444442 Calculate the square root of the right side: 22.370615647 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 22.370615647 and -22.370615647.Subproblem 1
x + -0.6666666665 = 22.370615647 Simplifying x + -0.6666666665 = 22.370615647 Reorder the terms: -0.6666666665 + x = 22.370615647 Solving -0.6666666665 + x = 22.370615647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 22.370615647 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 22.370615647 + 0.6666666665 x = 22.370615647 + 0.6666666665 Combine like terms: 22.370615647 + 0.6666666665 = 23.0372823135 x = 23.0372823135 Simplifying x = 23.0372823135Subproblem 2
x + -0.6666666665 = -22.370615647 Simplifying x + -0.6666666665 = -22.370615647 Reorder the terms: -0.6666666665 + x = -22.370615647 Solving -0.6666666665 + x = -22.370615647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -22.370615647 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -22.370615647 + 0.6666666665 x = -22.370615647 + 0.6666666665 Combine like terms: -22.370615647 + 0.6666666665 = -21.7039489805 x = -21.7039489805 Simplifying x = -21.7039489805Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.0372823135, -21.7039489805}
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