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Simplifying 4x2 = 30 + -10x Solving 4x2 = 30 + -10x Solving for variable 'x'. Reorder the terms: -30 + 10x + 4x2 = 30 + -10x + -30 + 10x Reorder the terms: -30 + 10x + 4x2 = 30 + -30 + -10x + 10x Combine like terms: 30 + -30 = 0 -30 + 10x + 4x2 = 0 + -10x + 10x -30 + 10x + 4x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -30 + 10x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 5x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -15 + 5x + 2x2 = 0 Solving -15 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 2.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 2.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 2.5x + x2 = 0 + 7.5 2.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 2.5x + x2 = 7.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 7.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 7.5 + 1.5625 Combine like terms: 7.5 + 1.5625 = 9.0625 1.5625 + 2.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + 1.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + 1.25 = 3.010398645 Simplifying x + 1.25 = 3.010398645 Reorder the terms: 1.25 + x = 3.010398645 Solving 1.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.010398645 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.010398645 + -1.25 x = 3.010398645 + -1.25 Combine like terms: 3.010398645 + -1.25 = 1.760398645 x = 1.760398645 Simplifying x = 1.760398645Subproblem 2
x + 1.25 = -3.010398645 Simplifying x + 1.25 = -3.010398645 Reorder the terms: 1.25 + x = -3.010398645 Solving 1.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.010398645 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.010398645 + -1.25 x = -3.010398645 + -1.25 Combine like terms: -3.010398645 + -1.25 = -4.260398645 x = -4.260398645 Simplifying x = -4.260398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.760398645, -4.260398645}Solution
x = {1.760398645, -4.260398645}
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