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Simplifying 10.5x2 + 0.473x + -0.0234 = 0 Reorder the terms: -0.0234 + 0.473x + 10.5x2 = 0 Solving -0.0234 + 0.473x + 10.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10.5 the coefficient of the squared term: Divide each side by '10.5'. -0.002228571429 + 0.04504761905x + x2 = 0 Move the constant term to the right: Add '0.002228571429' to each side of the equation. -0.002228571429 + 0.04504761905x + 0.002228571429 + x2 = 0 + 0.002228571429 Reorder the terms: -0.002228571429 + 0.002228571429 + 0.04504761905x + x2 = 0 + 0.002228571429 Combine like terms: -0.002228571429 + 0.002228571429 = 0.000000000000 0.000000000000 + 0.04504761905x + x2 = 0 + 0.002228571429 0.04504761905x + x2 = 0 + 0.002228571429 Combine like terms: 0 + 0.002228571429 = 0.002228571429 0.04504761905x + x2 = 0.002228571429 The x term is 0.04504761905x. Take half its coefficient (0.02252380953). Square it (0.0005073219957) and add it to both sides. Add '0.0005073219957' to each side of the equation. 0.04504761905x + 0.0005073219957 + x2 = 0.002228571429 + 0.0005073219957 Reorder the terms: 0.0005073219957 + 0.04504761905x + x2 = 0.002228571429 + 0.0005073219957 Combine like terms: 0.002228571429 + 0.0005073219957 = 0.0027358934247 0.0005073219957 + 0.04504761905x + x2 = 0.0027358934247 Factor a perfect square on the left side: (x + 0.02252380953)(x + 0.02252380953) = 0.0027358934247 Calculate the square root of the right side: 0.052305769 Break this problem into two subproblems by setting (x + 0.02252380953) equal to 0.052305769 and -0.052305769.Subproblem 1
x + 0.02252380953 = 0.052305769 Simplifying x + 0.02252380953 = 0.052305769 Reorder the terms: 0.02252380953 + x = 0.052305769 Solving 0.02252380953 + x = 0.052305769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02252380953' to each side of the equation. 0.02252380953 + -0.02252380953 + x = 0.052305769 + -0.02252380953 Combine like terms: 0.02252380953 + -0.02252380953 = 0.00000000000 0.00000000000 + x = 0.052305769 + -0.02252380953 x = 0.052305769 + -0.02252380953 Combine like terms: 0.052305769 + -0.02252380953 = 0.02978195947 x = 0.02978195947 Simplifying x = 0.02978195947Subproblem 2
x + 0.02252380953 = -0.052305769 Simplifying x + 0.02252380953 = -0.052305769 Reorder the terms: 0.02252380953 + x = -0.052305769 Solving 0.02252380953 + x = -0.052305769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02252380953' to each side of the equation. 0.02252380953 + -0.02252380953 + x = -0.052305769 + -0.02252380953 Combine like terms: 0.02252380953 + -0.02252380953 = 0.00000000000 0.00000000000 + x = -0.052305769 + -0.02252380953 x = -0.052305769 + -0.02252380953 Combine like terms: -0.052305769 + -0.02252380953 = -0.07482957853 x = -0.07482957853 Simplifying x = -0.07482957853Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.02978195947, -0.07482957853}
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