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Simplifying 3x2 + -30x = 75 Reorder the terms: -30x + 3x2 = 75 Solving -30x + 3x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + -30x + 3x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + -10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-25 + -10x + x2)' equal to zero and attempt to solve: Simplifying -25 + -10x + x2 = 0 Solving -25 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -10x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -10x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -10x + x2 = 0 + 25 -10x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -10x + x2 = 25 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 25 + 25 Reorder the terms: 25 + -10x + x2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + -10x + x2 = 50 Factor a perfect square on the left side: (x + -5)(x + -5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -5) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -5 = 7.071067812 Simplifying x + -5 = 7.071067812 Reorder the terms: -5 + x = 7.071067812 Solving -5 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.071067812 + 5 x = 7.071067812 + 5 Combine like terms: 7.071067812 + 5 = 12.071067812 x = 12.071067812 Simplifying x = 12.071067812Subproblem 2
x + -5 = -7.071067812 Simplifying x + -5 = -7.071067812 Reorder the terms: -5 + x = -7.071067812 Solving -5 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.071067812 + 5 x = -7.071067812 + 5 Combine like terms: -7.071067812 + 5 = -2.071067812 x = -2.071067812 Simplifying x = -2.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.071067812, -2.071067812}Solution
x = {12.071067812, -2.071067812}
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