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Simplifying 4x2 + -6x + -250 = 0 Reorder the terms: -250 + -6x + 4x2 = 0 Solving -250 + -6x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-125 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-125 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -125 + -3x + 2x2 = 0 Solving -125 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -62.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + -1.5x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + -1.5x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + -1.5x + x2 = 0 + 62.5 -1.5x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 -1.5x + x2 = 62.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 62.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 62.5 + 0.5625 Combine like terms: 62.5 + 0.5625 = 63.0625 0.5625 + -1.5x + x2 = 63.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 63.0625 Calculate the square root of the right side: 7.941190087 Break this problem into two subproblems by setting (x + -0.75) equal to 7.941190087 and -7.941190087.Subproblem 1
x + -0.75 = 7.941190087 Simplifying x + -0.75 = 7.941190087 Reorder the terms: -0.75 + x = 7.941190087 Solving -0.75 + x = 7.941190087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 7.941190087 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.941190087 + 0.75 x = 7.941190087 + 0.75 Combine like terms: 7.941190087 + 0.75 = 8.691190087 x = 8.691190087 Simplifying x = 8.691190087Subproblem 2
x + -0.75 = -7.941190087 Simplifying x + -0.75 = -7.941190087 Reorder the terms: -0.75 + x = -7.941190087 Solving -0.75 + x = -7.941190087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -7.941190087 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.941190087 + 0.75 x = -7.941190087 + 0.75 Combine like terms: -7.941190087 + 0.75 = -7.191190087 x = -7.191190087 Simplifying x = -7.191190087Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.691190087, -7.191190087}Solution
x = {8.691190087, -7.191190087}
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