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Simplifying 6x2 + 90x + -540 = 0 Reorder the terms: -540 + 90x + 6x2 = 0 Solving -540 + 90x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-90 + 15x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-90 + 15x + x2)' equal to zero and attempt to solve: Simplifying -90 + 15x + x2 = 0 Solving -90 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 15x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 15x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 15x + x2 = 0 + 90 15x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 15x + x2 = 90 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 90 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 90 + 56.25 Combine like terms: 90 + 56.25 = 146.25 56.25 + 15x + x2 = 146.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + 7.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + 7.5 = 12.093386622 Simplifying x + 7.5 = 12.093386622 Reorder the terms: 7.5 + x = 12.093386622 Solving 7.5 + x = 12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 12.093386622 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 12.093386622 + -7.5 x = 12.093386622 + -7.5 Combine like terms: 12.093386622 + -7.5 = 4.593386622 x = 4.593386622 Simplifying x = 4.593386622Subproblem 2
x + 7.5 = -12.093386622 Simplifying x + 7.5 = -12.093386622 Reorder the terms: 7.5 + x = -12.093386622 Solving 7.5 + x = -12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -12.093386622 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -12.093386622 + -7.5 x = -12.093386622 + -7.5 Combine like terms: -12.093386622 + -7.5 = -19.593386622 x = -19.593386622 Simplifying x = -19.593386622Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.593386622, -19.593386622}Solution
x = {4.593386622, -19.593386622}
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