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Simplifying 0.4x2 + -5x + 15 = 0 Reorder the terms: 15 + -5x + 0.4x2 = 0 Solving 15 + -5x + 0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 37.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -12.5x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -12.5x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -12.5x + x2 = 0 + -37.5 -12.5x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -12.5x + x2 = -37.5 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -37.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -37.5 + 39.0625 Combine like terms: -37.5 + 39.0625 = 1.5625 39.0625 + -12.5x + x2 = 1.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x + -6.25) equal to 1.25 and -1.25.Subproblem 1
x + -6.25 = 1.25 Simplifying x + -6.25 = 1.25 Reorder the terms: -6.25 + x = 1.25 Solving -6.25 + x = 1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 1.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 1.25 + 6.25 x = 1.25 + 6.25 Combine like terms: 1.25 + 6.25 = 7.5 x = 7.5 Simplifying x = 7.5Subproblem 2
x + -6.25 = -1.25 Simplifying x + -6.25 = -1.25 Reorder the terms: -6.25 + x = -1.25 Solving -6.25 + x = -1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -1.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -1.25 + 6.25 x = -1.25 + 6.25 Combine like terms: -1.25 + 6.25 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.5, 5}
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