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Simplifying 10x2 + -9x + -15 = 0 Reorder the terms: -15 + -9x + 10x2 = 0 Solving -15 + -9x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + -0.9x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.9x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.9x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.9x + x2 = 0 + 1.5 -0.9x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.9x + x2 = 1.5 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = 1.5 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = 1.5 + 0.2025 Combine like terms: 1.5 + 0.2025 = 1.7025 0.2025 + -0.9x + x2 = 1.7025 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 1.7025 Calculate the square root of the right side: 1.304798835 Break this problem into two subproblems by setting (x + -0.45) equal to 1.304798835 and -1.304798835.Subproblem 1
x + -0.45 = 1.304798835 Simplifying x + -0.45 = 1.304798835 Reorder the terms: -0.45 + x = 1.304798835 Solving -0.45 + x = 1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 1.304798835 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 1.304798835 + 0.45 x = 1.304798835 + 0.45 Combine like terms: 1.304798835 + 0.45 = 1.754798835 x = 1.754798835 Simplifying x = 1.754798835Subproblem 2
x + -0.45 = -1.304798835 Simplifying x + -0.45 = -1.304798835 Reorder the terms: -0.45 + x = -1.304798835 Solving -0.45 + x = -1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -1.304798835 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -1.304798835 + 0.45 x = -1.304798835 + 0.45 Combine like terms: -1.304798835 + 0.45 = -0.854798835 x = -0.854798835 Simplifying x = -0.854798835Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.754798835, -0.854798835}
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