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Simplifying 3x2 + -90x + 525 = 0 Reorder the terms: 525 + -90x + 3x2 = 0 Solving 525 + -90x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(175 + -30x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(175 + -30x + x2)' equal to zero and attempt to solve: Simplifying 175 + -30x + x2 = 0 Solving 175 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-175' to each side of the equation. 175 + -30x + -175 + x2 = 0 + -175 Reorder the terms: 175 + -175 + -30x + x2 = 0 + -175 Combine like terms: 175 + -175 = 0 0 + -30x + x2 = 0 + -175 -30x + x2 = 0 + -175 Combine like terms: 0 + -175 = -175 -30x + x2 = -175 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 = -175 + 225 Reorder the terms: 225 + -30x + x2 = -175 + 225 Combine like terms: -175 + 225 = 50 225 + -30x + x2 = 50 Factor a perfect square on the left side: (x + -15)(x + -15) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -15) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -15 = 7.071067812 Simplifying x + -15 = 7.071067812 Reorder the terms: -15 + x = 7.071067812 Solving -15 + x = 7.071067812 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 = 7.071067812 + 15 Combine like terms: -15 + 15 = 0 0 + x = 7.071067812 + 15 x = 7.071067812 + 15 Combine like terms: 7.071067812 + 15 = 22.071067812 x = 22.071067812 Simplifying x = 22.071067812Subproblem 2
x + -15 = -7.071067812 Simplifying x + -15 = -7.071067812 Reorder the terms: -15 + x = -7.071067812 Solving -15 + x = -7.071067812 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 = -7.071067812 + 15 Combine like terms: -15 + 15 = 0 0 + x = -7.071067812 + 15 x = -7.071067812 + 15 Combine like terms: -7.071067812 + 15 = 7.928932188 x = 7.928932188 Simplifying x = 7.928932188Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.071067812, 7.928932188}Solution
x = {22.071067812, 7.928932188}
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