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Simplifying 30x2 + -464x + -2500 = 0 Reorder the terms: -2500 + -464x + 30x2 = 0 Solving -2500 + -464x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1250 + -232x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1250 + -232x + 15x2)' equal to zero and attempt to solve: Simplifying -1250 + -232x + 15x2 = 0 Solving -1250 + -232x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -83.33333333 + -15.46666667x + x2 = 0 Move the constant term to the right: Add '83.33333333' to each side of the equation. -83.33333333 + -15.46666667x + 83.33333333 + x2 = 0 + 83.33333333 Reorder the terms: -83.33333333 + 83.33333333 + -15.46666667x + x2 = 0 + 83.33333333 Combine like terms: -83.33333333 + 83.33333333 = 0.00000000 0.00000000 + -15.46666667x + x2 = 0 + 83.33333333 -15.46666667x + x2 = 0 + 83.33333333 Combine like terms: 0 + 83.33333333 = 83.33333333 -15.46666667x + x2 = 83.33333333 The x term is -15.46666667x. Take half its coefficient (-7.733333335). Square it (59.80444447) and add it to both sides. Add '59.80444447' to each side of the equation. -15.46666667x + 59.80444447 + x2 = 83.33333333 + 59.80444447 Reorder the terms: 59.80444447 + -15.46666667x + x2 = 83.33333333 + 59.80444447 Combine like terms: 83.33333333 + 59.80444447 = 143.1377778 59.80444447 + -15.46666667x + x2 = 143.1377778 Factor a perfect square on the left side: (x + -7.733333335)(x + -7.733333335) = 143.1377778 Calculate the square root of the right side: 11.964020135 Break this problem into two subproblems by setting (x + -7.733333335) equal to 11.964020135 and -11.964020135.Subproblem 1
x + -7.733333335 = 11.964020135 Simplifying x + -7.733333335 = 11.964020135 Reorder the terms: -7.733333335 + x = 11.964020135 Solving -7.733333335 + x = 11.964020135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.733333335' to each side of the equation. -7.733333335 + 7.733333335 + x = 11.964020135 + 7.733333335 Combine like terms: -7.733333335 + 7.733333335 = 0.000000000 0.000000000 + x = 11.964020135 + 7.733333335 x = 11.964020135 + 7.733333335 Combine like terms: 11.964020135 + 7.733333335 = 19.69735347 x = 19.69735347 Simplifying x = 19.69735347Subproblem 2
x + -7.733333335 = -11.964020135 Simplifying x + -7.733333335 = -11.964020135 Reorder the terms: -7.733333335 + x = -11.964020135 Solving -7.733333335 + x = -11.964020135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.733333335' to each side of the equation. -7.733333335 + 7.733333335 + x = -11.964020135 + 7.733333335 Combine like terms: -7.733333335 + 7.733333335 = 0.000000000 0.000000000 + x = -11.964020135 + 7.733333335 x = -11.964020135 + 7.733333335 Combine like terms: -11.964020135 + 7.733333335 = -4.2306868 x = -4.2306868 Simplifying x = -4.2306868Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.69735347, -4.2306868}Solution
x = {19.69735347, -4.2306868}
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