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Simplifying x = 2.3x2 + -9 Reorder the terms: x = -9 + 2.3x2 Solving x = -9 + 2.3x2 Solving for variable 'x'. Reorder the terms: 9 + x + -2.3x2 = -9 + 2.3x2 + 9 + -2.3x2 Reorder the terms: 9 + x + -2.3x2 = -9 + 9 + 2.3x2 + -2.3x2 Combine like terms: -9 + 9 = 0 9 + x + -2.3x2 = 0 + 2.3x2 + -2.3x2 9 + x + -2.3x2 = 2.3x2 + -2.3x2 Combine like terms: 2.3x2 + -2.3x2 = 0.0 9 + x + -2.3x2 = 0.0 Begin completing the square. Divide all terms by -2.3 the coefficient of the squared term: Divide each side by '-2.3'. -3.913043478 + -0.4347826087x + x2 = 0 Move the constant term to the right: Add '3.913043478' to each side of the equation. -3.913043478 + -0.4347826087x + 3.913043478 + x2 = 0 + 3.913043478 Reorder the terms: -3.913043478 + 3.913043478 + -0.4347826087x + x2 = 0 + 3.913043478 Combine like terms: -3.913043478 + 3.913043478 = 0.000000000 0.000000000 + -0.4347826087x + x2 = 0 + 3.913043478 -0.4347826087x + x2 = 0 + 3.913043478 Combine like terms: 0 + 3.913043478 = 3.913043478 -0.4347826087x + x2 = 3.913043478 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.4347826087x + 0.25 + x2 = 3.913043478 + 0.25 Reorder the terms: 0.25 + -0.4347826087x + x2 = 3.913043478 + 0.25 Combine like terms: 3.913043478 + 0.25 = 4.163043478 0.25 + -0.4347826087x + x2 = 4.163043478 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.163043478 Calculate the square root of the right side: 2.040353763 Break this problem into two subproblems by setting (x + 0.5) equal to 2.040353763 and -2.040353763.Subproblem 1
x + 0.5 = 2.040353763 Simplifying x + 0.5 = 2.040353763 Reorder the terms: 0.5 + x = 2.040353763 Solving 0.5 + x = 2.040353763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.040353763 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.040353763 + -0.5 x = 2.040353763 + -0.5 Combine like terms: 2.040353763 + -0.5 = 1.540353763 x = 1.540353763 Simplifying x = 1.540353763Subproblem 2
x + 0.5 = -2.040353763 Simplifying x + 0.5 = -2.040353763 Reorder the terms: 0.5 + x = -2.040353763 Solving 0.5 + x = -2.040353763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.040353763 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.040353763 + -0.5 x = -2.040353763 + -0.5 Combine like terms: -2.040353763 + -0.5 = -2.540353763 x = -2.540353763 Simplifying x = -2.540353763Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.540353763, -2.540353763}
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