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Simplifying -5x2 + -1x + 9 = 0 Reorder the terms: 9 + -1x + -5x2 = 0 Solving 9 + -1x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.8 + 0.2x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.2x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.2x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.2x + x2 = 0 + 1.8 0.2x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.2x + x2 = 1.8 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 1.8 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 1.8 + 0.01 Combine like terms: 1.8 + 0.01 = 1.81 0.01 + 0.2x + x2 = 1.81 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 1.81 Calculate the square root of the right side: 1.345362405 Break this problem into two subproblems by setting (x + 0.1) equal to 1.345362405 and -1.345362405.Subproblem 1
x + 0.1 = 1.345362405 Simplifying x + 0.1 = 1.345362405 Reorder the terms: 0.1 + x = 1.345362405 Solving 0.1 + x = 1.345362405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.345362405 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.345362405 + -0.1 x = 1.345362405 + -0.1 Combine like terms: 1.345362405 + -0.1 = 1.245362405 x = 1.245362405 Simplifying x = 1.245362405Subproblem 2
x + 0.1 = -1.345362405 Simplifying x + 0.1 = -1.345362405 Reorder the terms: 0.1 + x = -1.345362405 Solving 0.1 + x = -1.345362405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.345362405 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.345362405 + -0.1 x = -1.345362405 + -0.1 Combine like terms: -1.345362405 + -0.1 = -1.445362405 x = -1.445362405 Simplifying x = -1.445362405Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.245362405, -1.445362405}
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