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Simplifying 2x2 + -15x + 8 = 0 Reorder the terms: 8 + -15x + 2x2 = 0 Solving 8 + -15x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -7.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -7.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7.5x + x2 = 0 + -4 -7.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7.5x + x2 = -4 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -4 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -4 + 14.0625 Combine like terms: -4 + 14.0625 = 10.0625 14.0625 + -7.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + -3.75) equal to 3.172144385 and -3.172144385.Subproblem 1
x + -3.75 = 3.172144385 Simplifying x + -3.75 = 3.172144385 Reorder the terms: -3.75 + x = 3.172144385 Solving -3.75 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 3.172144385 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.172144385 + 3.75 x = 3.172144385 + 3.75 Combine like terms: 3.172144385 + 3.75 = 6.922144385 x = 6.922144385 Simplifying x = 6.922144385Subproblem 2
x + -3.75 = -3.172144385 Simplifying x + -3.75 = -3.172144385 Reorder the terms: -3.75 + x = -3.172144385 Solving -3.75 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -3.172144385 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.172144385 + 3.75 x = -3.172144385 + 3.75 Combine like terms: -3.172144385 + 3.75 = 0.577855615 x = 0.577855615 Simplifying x = 0.577855615Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.922144385, 0.577855615}
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