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Simplifying 3x2 + -90x + 300 = 0 Reorder the terms: 300 + -90x + 3x2 = 0 Solving 300 + -90x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(100 + -30x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(100 + -30x + x2)' equal to zero and attempt to solve: Simplifying 100 + -30x + x2 = 0 Solving 100 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -30x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -30x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -30x + x2 = 0 + -100 -30x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -30x + x2 = -100 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 = -100 + 225 Reorder the terms: 225 + -30x + x2 = -100 + 225 Combine like terms: -100 + 225 = 125 225 + -30x + x2 = 125 Factor a perfect square on the left side: (x + -15)(x + -15) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -15) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -15 = 11.180339887 Simplifying x + -15 = 11.180339887 Reorder the terms: -15 + x = 11.180339887 Solving -15 + x = 11.180339887 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 = 11.180339887 + 15 Combine like terms: -15 + 15 = 0 0 + x = 11.180339887 + 15 x = 11.180339887 + 15 Combine like terms: 11.180339887 + 15 = 26.180339887 x = 26.180339887 Simplifying x = 26.180339887Subproblem 2
x + -15 = -11.180339887 Simplifying x + -15 = -11.180339887 Reorder the terms: -15 + x = -11.180339887 Solving -15 + x = -11.180339887 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 = -11.180339887 + 15 Combine like terms: -15 + 15 = 0 0 + x = -11.180339887 + 15 x = -11.180339887 + 15 Combine like terms: -11.180339887 + 15 = 3.819660113 x = 3.819660113 Simplifying x = 3.819660113Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.180339887, 3.819660113}Solution
x = {26.180339887, 3.819660113}
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