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Simplifying 0 = 2x2 + -15x + 5 Reorder the terms: 0 = 5 + -15x + 2x2 Solving 0 = 5 + -15x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + 15x + -2x2 = 5 + -15x + 2x2 + -5 + 15x + -2x2 Reorder the terms: -5 + 15x + -2x2 = 5 + -5 + -15x + 15x + 2x2 + -2x2 Combine like terms: 5 + -5 = 0 -5 + 15x + -2x2 = 0 + -15x + 15x + 2x2 + -2x2 -5 + 15x + -2x2 = -15x + 15x + 2x2 + -2x2 Combine like terms: -15x + 15x = 0 -5 + 15x + -2x2 = 0 + 2x2 + -2x2 -5 + 15x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + 15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -7.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -7.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -7.5x + x2 = 0 + -2.5 -7.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -7.5x + x2 = -2.5 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 = -2.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -2.5 + 14.0625 Combine like terms: -2.5 + 14.0625 = 11.5625 14.0625 + -7.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + -3.75) equal to 3.400367627 and -3.400367627.Subproblem 1
x + -3.75 = 3.400367627 Simplifying x + -3.75 = 3.400367627 Reorder the terms: -3.75 + x = 3.400367627 Solving -3.75 + x = 3.400367627 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 = 3.400367627 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.400367627 + 3.75 x = 3.400367627 + 3.75 Combine like terms: 3.400367627 + 3.75 = 7.150367627 x = 7.150367627 Simplifying x = 7.150367627Subproblem 2
x + -3.75 = -3.400367627 Simplifying x + -3.75 = -3.400367627 Reorder the terms: -3.75 + x = -3.400367627 Solving -3.75 + x = -3.400367627 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 = -3.400367627 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.400367627 + 3.75 x = -3.400367627 + 3.75 Combine like terms: -3.400367627 + 3.75 = 0.349632373 x = 0.349632373 Simplifying x = 0.349632373Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.150367627, 0.349632373}
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