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Simplifying 4x2 + -120x + 30 = 0 Reorder the terms: 30 + -120x + 4x2 = 0 Solving 30 + -120x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -60x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -60x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + -60x + 2x2 = 0 Solving 15 + -60x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -30x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -30x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -30x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -30x + x2 = 0 + -7.5 -30x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -30x + x2 = -7.5 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -7.5 + 225 Reorder the terms: 225 + -30x + x2 = -7.5 + 225 Combine like terms: -7.5 + 225 = 217.5 225 + -30x + x2 = 217.5 Factor a perfect square on the left side: (x + -15)(x + -15) = 217.5 Calculate the square root of the right side: 14.747881204 Break this problem into two subproblems by setting (x + -15) equal to 14.747881204 and -14.747881204.Subproblem 1
x + -15 = 14.747881204 Simplifying x + -15 = 14.747881204 Reorder the terms: -15 + x = 14.747881204 Solving -15 + x = 14.747881204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 14.747881204 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.747881204 + 15 x = 14.747881204 + 15 Combine like terms: 14.747881204 + 15 = 29.747881204 x = 29.747881204 Simplifying x = 29.747881204Subproblem 2
x + -15 = -14.747881204 Simplifying x + -15 = -14.747881204 Reorder the terms: -15 + x = -14.747881204 Solving -15 + x = -14.747881204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -14.747881204 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.747881204 + 15 x = -14.747881204 + 15 Combine like terms: -14.747881204 + 15 = 0.252118796 x = 0.252118796 Simplifying x = 0.252118796Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.747881204, 0.252118796}Solution
x = {29.747881204, 0.252118796}
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