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Simplifying 2x2 + -60x + 10 = 0 Reorder the terms: 10 + -60x + 2x2 = 0 Solving 10 + -60x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -30x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -30x + x2)' equal to zero and attempt to solve: Simplifying 5 + -30x + x2 = 0 Solving 5 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -30x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -30x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -30x + x2 = 0 + -5 -30x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -30x + x2 = -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 = -5 + 225 Reorder the terms: 225 + -30x + x2 = -5 + 225 Combine like terms: -5 + 225 = 220 225 + -30x + x2 = 220 Factor a perfect square on the left side: (x + -15)(x + -15) = 220 Calculate the square root of the right side: 14.832396974 Break this problem into two subproblems by setting (x + -15) equal to 14.832396974 and -14.832396974.Subproblem 1
x + -15 = 14.832396974 Simplifying x + -15 = 14.832396974 Reorder the terms: -15 + x = 14.832396974 Solving -15 + x = 14.832396974 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 = 14.832396974 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.832396974 + 15 x = 14.832396974 + 15 Combine like terms: 14.832396974 + 15 = 29.832396974 x = 29.832396974 Simplifying x = 29.832396974Subproblem 2
x + -15 = -14.832396974 Simplifying x + -15 = -14.832396974 Reorder the terms: -15 + x = -14.832396974 Solving -15 + x = -14.832396974 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 = -14.832396974 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.832396974 + 15 x = -14.832396974 + 15 Combine like terms: -14.832396974 + 15 = 0.167603026 x = 0.167603026 Simplifying x = 0.167603026Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.832396974, 0.167603026}Solution
x = {29.832396974, 0.167603026}
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