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Simplifying 0.2x2 + 0.32x + -0.15 = 0 Reorder the terms: -0.15 + 0.32x + 0.2x2 = 0 Solving -0.15 + 0.32x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -0.75 + 1.6x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.6x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.6x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.6x + x2 = 0 + 0.75 1.6x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.6x + x2 = 0.75 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 0.75 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 0.75 + 0.64 Combine like terms: 0.75 + 0.64 = 1.39 0.64 + 1.6x + x2 = 1.39 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 1.39 Calculate the square root of the right side: 1.178982612 Break this problem into two subproblems by setting (x + 0.8) equal to 1.178982612 and -1.178982612.Subproblem 1
x + 0.8 = 1.178982612 Simplifying x + 0.8 = 1.178982612 Reorder the terms: 0.8 + x = 1.178982612 Solving 0.8 + x = 1.178982612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.178982612 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.178982612 + -0.8 x = 1.178982612 + -0.8 Combine like terms: 1.178982612 + -0.8 = 0.378982612 x = 0.378982612 Simplifying x = 0.378982612Subproblem 2
x + 0.8 = -1.178982612 Simplifying x + 0.8 = -1.178982612 Reorder the terms: 0.8 + x = -1.178982612 Solving 0.8 + x = -1.178982612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.178982612 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.178982612 + -0.8 x = -1.178982612 + -0.8 Combine like terms: -1.178982612 + -0.8 = -1.978982612 x = -1.978982612 Simplifying x = -1.978982612Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.378982612, -1.978982612}
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