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Simplifying 756x2 + -3032x + -444 = 0 Reorder the terms: -444 + -3032x + 756x2 = 0 Solving -444 + -3032x + 756x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-111 + -758x + 189x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-111 + -758x + 189x2)' equal to zero and attempt to solve: Simplifying -111 + -758x + 189x2 = 0 Solving -111 + -758x + 189x2 = 0 Begin completing the square. Divide all terms by 189 the coefficient of the squared term: Divide each side by '189'. -0.5873015873 + -4.010582011x + x2 = 0 Move the constant term to the right: Add '0.5873015873' to each side of the equation. -0.5873015873 + -4.010582011x + 0.5873015873 + x2 = 0 + 0.5873015873 Reorder the terms: -0.5873015873 + 0.5873015873 + -4.010582011x + x2 = 0 + 0.5873015873 Combine like terms: -0.5873015873 + 0.5873015873 = 0.0000000000 0.0000000000 + -4.010582011x + x2 = 0 + 0.5873015873 -4.010582011x + x2 = 0 + 0.5873015873 Combine like terms: 0 + 0.5873015873 = 0.5873015873 -4.010582011x + x2 = 0.5873015873 The x term is -4.010582011x. Take half its coefficient (-2.005291006). Square it (4.021192019) and add it to both sides. Add '4.021192019' to each side of the equation. -4.010582011x + 4.021192019 + x2 = 0.5873015873 + 4.021192019 Reorder the terms: 4.021192019 + -4.010582011x + x2 = 0.5873015873 + 4.021192019 Combine like terms: 0.5873015873 + 4.021192019 = 4.6084936063 4.021192019 + -4.010582011x + x2 = 4.6084936063 Factor a perfect square on the left side: (x + -2.005291006)(x + -2.005291006) = 4.6084936063 Calculate the square root of the right side: 2.146740228 Break this problem into two subproblems by setting (x + -2.005291006) equal to 2.146740228 and -2.146740228.Subproblem 1
x + -2.005291006 = 2.146740228 Simplifying x + -2.005291006 = 2.146740228 Reorder the terms: -2.005291006 + x = 2.146740228 Solving -2.005291006 + x = 2.146740228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.005291006' to each side of the equation. -2.005291006 + 2.005291006 + x = 2.146740228 + 2.005291006 Combine like terms: -2.005291006 + 2.005291006 = 0.000000000 0.000000000 + x = 2.146740228 + 2.005291006 x = 2.146740228 + 2.005291006 Combine like terms: 2.146740228 + 2.005291006 = 4.152031234 x = 4.152031234 Simplifying x = 4.152031234Subproblem 2
x + -2.005291006 = -2.146740228 Simplifying x + -2.005291006 = -2.146740228 Reorder the terms: -2.005291006 + x = -2.146740228 Solving -2.005291006 + x = -2.146740228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.005291006' to each side of the equation. -2.005291006 + 2.005291006 + x = -2.146740228 + 2.005291006 Combine like terms: -2.005291006 + 2.005291006 = 0.000000000 0.000000000 + x = -2.146740228 + 2.005291006 x = -2.146740228 + 2.005291006 Combine like terms: -2.146740228 + 2.005291006 = -0.141449222 x = -0.141449222 Simplifying x = -0.141449222Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.152031234, -0.141449222}Solution
x = {4.152031234, -0.141449222}
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