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Simplifying 4x(7x + -10) + 60 + 90 = 360 Reorder the terms: 4x(-10 + 7x) + 60 + 90 = 360 (-10 * 4x + 7x * 4x) + 60 + 90 = 360 (-40x + 28x2) + 60 + 90 = 360 Reorder the terms: 60 + 90 + -40x + 28x2 = 360 Combine like terms: 60 + 90 = 150 150 + -40x + 28x2 = 360 Solving 150 + -40x + 28x2 = 360 Solving for variable 'x'. Reorder the terms: 150 + -360 + -40x + 28x2 = 360 + -360 Combine like terms: 150 + -360 = -210 -210 + -40x + 28x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -210 + -40x + 28x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-105 + -20x + 14x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-105 + -20x + 14x2)' equal to zero and attempt to solve: Simplifying -105 + -20x + 14x2 = 0 Solving -105 + -20x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -7.5 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -1.428571429x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -1.428571429x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -1.428571429x + x2 = 0 + 7.5 -1.428571429x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -1.428571429x + x2 = 7.5 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 7.5 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 7.5 + 0.5102040819 Combine like terms: 7.5 + 0.5102040819 = 8.0102040819 0.5102040819 + -1.428571429x + x2 = 8.0102040819 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 8.0102040819 Calculate the square root of the right side: 2.830230394 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 2.830230394 and -2.830230394.Subproblem 1
x + -0.7142857145 = 2.830230394 Simplifying x + -0.7142857145 = 2.830230394 Reorder the terms: -0.7142857145 + x = 2.830230394 Solving -0.7142857145 + x = 2.830230394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 2.830230394 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 2.830230394 + 0.7142857145 x = 2.830230394 + 0.7142857145 Combine like terms: 2.830230394 + 0.7142857145 = 3.5445161085 x = 3.5445161085 Simplifying x = 3.5445161085Subproblem 2
x + -0.7142857145 = -2.830230394 Simplifying x + -0.7142857145 = -2.830230394 Reorder the terms: -0.7142857145 + x = -2.830230394 Solving -0.7142857145 + x = -2.830230394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -2.830230394 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -2.830230394 + 0.7142857145 x = -2.830230394 + 0.7142857145 Combine like terms: -2.830230394 + 0.7142857145 = -2.1159446795 x = -2.1159446795 Simplifying x = -2.1159446795Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5445161085, -2.1159446795}Solution
x = {3.5445161085, -2.1159446795}
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