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Simplifying 288 = 6x2 + 30x Reorder the terms: 288 = 30x + 6x2 Solving 288 = 30x + 6x2 Solving for variable 'x'. Reorder the terms: 288 + -30x + -6x2 = 30x + -30x + 6x2 + -6x2 Combine like terms: 30x + -30x = 0 288 + -30x + -6x2 = 0 + 6x2 + -6x2 288 + -30x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 288 + -30x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(48 + -5x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(48 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 48 + -5x + -1x2 = 0 Solving 48 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 5x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 5x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 5x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 5x + x2 = 0 + 48 5x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 5x + x2 = 48 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 48 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 48 + 6.25 Combine like terms: 48 + 6.25 = 54.25 6.25 + 5x + x2 = 54.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + 2.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + 2.5 = 7.365459931 Simplifying x + 2.5 = 7.365459931 Reorder the terms: 2.5 + x = 7.365459931 Solving 2.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.365459931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.365459931 + -2.5 x = 7.365459931 + -2.5 Combine like terms: 7.365459931 + -2.5 = 4.865459931 x = 4.865459931 Simplifying x = 4.865459931Subproblem 2
x + 2.5 = -7.365459931 Simplifying x + 2.5 = -7.365459931 Reorder the terms: 2.5 + x = -7.365459931 Solving 2.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.365459931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.365459931 + -2.5 x = -7.365459931 + -2.5 Combine like terms: -7.365459931 + -2.5 = -9.865459931 x = -9.865459931 Simplifying x = -9.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.865459931, -9.865459931}Solution
x = {4.865459931, -9.865459931}
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