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Simplifying 4x2 + 60x + -300 = 0 Reorder the terms: -300 + 60x + 4x2 = 0 Solving -300 + 60x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-75 + 15x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-75 + 15x + x2)' equal to zero and attempt to solve: Simplifying -75 + 15x + x2 = 0 Solving -75 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 15x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 15x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 15x + x2 = 0 + 75 15x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 15x + x2 = 75 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 = 75 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 75 + 56.25 Combine like terms: 75 + 56.25 = 131.25 56.25 + 15x + x2 = 131.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (x + 7.5) equal to 11.456439237 and -11.456439237.Subproblem 1
x + 7.5 = 11.456439237 Simplifying x + 7.5 = 11.456439237 Reorder the terms: 7.5 + x = 11.456439237 Solving 7.5 + x = 11.456439237 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 = 11.456439237 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 11.456439237 + -7.5 x = 11.456439237 + -7.5 Combine like terms: 11.456439237 + -7.5 = 3.956439237 x = 3.956439237 Simplifying x = 3.956439237Subproblem 2
x + 7.5 = -11.456439237 Simplifying x + 7.5 = -11.456439237 Reorder the terms: 7.5 + x = -11.456439237 Solving 7.5 + x = -11.456439237 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 = -11.456439237 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -11.456439237 + -7.5 x = -11.456439237 + -7.5 Combine like terms: -11.456439237 + -7.5 = -18.956439237 x = -18.956439237 Simplifying x = -18.956439237Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.956439237, -18.956439237}Solution
x = {3.956439237, -18.956439237}
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