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Simplifying 44x2 + 250x + -12 = 0 Reorder the terms: -12 + 250x + 44x2 = 0 Solving -12 + 250x + 44x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 125x + 22x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 125x + 22x2)' equal to zero and attempt to solve: Simplifying -6 + 125x + 22x2 = 0 Solving -6 + 125x + 22x2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -0.2727272727 + 5.681818182x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + 5.681818182x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + 5.681818182x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + 5.681818182x + x2 = 0 + 0.2727272727 5.681818182x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 5.681818182x + x2 = 0.2727272727 The x term is 5.681818182x. Take half its coefficient (2.840909091). Square it (8.070764463) and add it to both sides. Add '8.070764463' to each side of the equation. 5.681818182x + 8.070764463 + x2 = 0.2727272727 + 8.070764463 Reorder the terms: 8.070764463 + 5.681818182x + x2 = 0.2727272727 + 8.070764463 Combine like terms: 0.2727272727 + 8.070764463 = 8.3434917357 8.070764463 + 5.681818182x + x2 = 8.3434917357 Factor a perfect square on the left side: (x + 2.840909091)(x + 2.840909091) = 8.3434917357 Calculate the square root of the right side: 2.888510297 Break this problem into two subproblems by setting (x + 2.840909091) equal to 2.888510297 and -2.888510297.Subproblem 1
x + 2.840909091 = 2.888510297 Simplifying x + 2.840909091 = 2.888510297 Reorder the terms: 2.840909091 + x = 2.888510297 Solving 2.840909091 + x = 2.888510297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.840909091' to each side of the equation. 2.840909091 + -2.840909091 + x = 2.888510297 + -2.840909091 Combine like terms: 2.840909091 + -2.840909091 = 0.000000000 0.000000000 + x = 2.888510297 + -2.840909091 x = 2.888510297 + -2.840909091 Combine like terms: 2.888510297 + -2.840909091 = 0.047601206 x = 0.047601206 Simplifying x = 0.047601206Subproblem 2
x + 2.840909091 = -2.888510297 Simplifying x + 2.840909091 = -2.888510297 Reorder the terms: 2.840909091 + x = -2.888510297 Solving 2.840909091 + x = -2.888510297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.840909091' to each side of the equation. 2.840909091 + -2.840909091 + x = -2.888510297 + -2.840909091 Combine like terms: 2.840909091 + -2.840909091 = 0.000000000 0.000000000 + x = -2.888510297 + -2.840909091 x = -2.888510297 + -2.840909091 Combine like terms: -2.888510297 + -2.840909091 = -5.729419388 x = -5.729419388 Simplifying x = -5.729419388Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.047601206, -5.729419388}Solution
x = {0.047601206, -5.729419388}
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