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Simplifying 10x2 + 24x + -576 = 0 Reorder the terms: -576 + 24x + 10x2 = 0 Solving -576 + 24x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-288 + 12x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-288 + 12x + 5x2)' equal to zero and attempt to solve: Simplifying -288 + 12x + 5x2 = 0 Solving -288 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -57.6 + 2.4x + x2 = 0 Move the constant term to the right: Add '57.6' to each side of the equation. -57.6 + 2.4x + 57.6 + x2 = 0 + 57.6 Reorder the terms: -57.6 + 57.6 + 2.4x + x2 = 0 + 57.6 Combine like terms: -57.6 + 57.6 = 0.0 0.0 + 2.4x + x2 = 0 + 57.6 2.4x + x2 = 0 + 57.6 Combine like terms: 0 + 57.6 = 57.6 2.4x + x2 = 57.6 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 57.6 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 57.6 + 1.44 Combine like terms: 57.6 + 1.44 = 59.04 1.44 + 2.4x + x2 = 59.04 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 59.04 Calculate the square root of the right side: 7.683749085 Break this problem into two subproblems by setting (x + 1.2) equal to 7.683749085 and -7.683749085.Subproblem 1
x + 1.2 = 7.683749085 Simplifying x + 1.2 = 7.683749085 Reorder the terms: 1.2 + x = 7.683749085 Solving 1.2 + x = 7.683749085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 7.683749085 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 7.683749085 + -1.2 x = 7.683749085 + -1.2 Combine like terms: 7.683749085 + -1.2 = 6.483749085 x = 6.483749085 Simplifying x = 6.483749085Subproblem 2
x + 1.2 = -7.683749085 Simplifying x + 1.2 = -7.683749085 Reorder the terms: 1.2 + x = -7.683749085 Solving 1.2 + x = -7.683749085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -7.683749085 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -7.683749085 + -1.2 x = -7.683749085 + -1.2 Combine like terms: -7.683749085 + -1.2 = -8.883749085 x = -8.883749085 Simplifying x = -8.883749085Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.483749085, -8.883749085}Solution
x = {6.483749085, -8.883749085}
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