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Simplifying 100x2 + 46.24x + -4.624 = 0 Reorder the terms: -4.624 + 46.24x + 100x2 = 0 Solving -4.624 + 46.24x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.04624 + 0.4624x + x2 = 0 Move the constant term to the right: Add '0.04624' to each side of the equation. -0.04624 + 0.4624x + 0.04624 + x2 = 0 + 0.04624 Reorder the terms: -0.04624 + 0.04624 + 0.4624x + x2 = 0 + 0.04624 Combine like terms: -0.04624 + 0.04624 = 0.00000 0.00000 + 0.4624x + x2 = 0 + 0.04624 0.4624x + x2 = 0 + 0.04624 Combine like terms: 0 + 0.04624 = 0.04624 0.4624x + x2 = 0.04624 The x term is 0.4624x. Take half its coefficient (0.2312). Square it (0.05345344) and add it to both sides. Add '0.05345344' to each side of the equation. 0.4624x + 0.05345344 + x2 = 0.04624 + 0.05345344 Reorder the terms: 0.05345344 + 0.4624x + x2 = 0.04624 + 0.05345344 Combine like terms: 0.04624 + 0.05345344 = 0.09969344 0.05345344 + 0.4624x + x2 = 0.09969344 Factor a perfect square on the left side: (x + 0.2312)(x + 0.2312) = 0.09969344 Calculate the square root of the right side: 0.31574268 Break this problem into two subproblems by setting (x + 0.2312) equal to 0.31574268 and -0.31574268.Subproblem 1
x + 0.2312 = 0.31574268 Simplifying x + 0.2312 = 0.31574268 Reorder the terms: 0.2312 + x = 0.31574268 Solving 0.2312 + x = 0.31574268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2312' to each side of the equation. 0.2312 + -0.2312 + x = 0.31574268 + -0.2312 Combine like terms: 0.2312 + -0.2312 = 0.0000 0.0000 + x = 0.31574268 + -0.2312 x = 0.31574268 + -0.2312 Combine like terms: 0.31574268 + -0.2312 = 0.08454268 x = 0.08454268 Simplifying x = 0.08454268Subproblem 2
x + 0.2312 = -0.31574268 Simplifying x + 0.2312 = -0.31574268 Reorder the terms: 0.2312 + x = -0.31574268 Solving 0.2312 + x = -0.31574268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2312' to each side of the equation. 0.2312 + -0.2312 + x = -0.31574268 + -0.2312 Combine like terms: 0.2312 + -0.2312 = 0.0000 0.0000 + x = -0.31574268 + -0.2312 x = -0.31574268 + -0.2312 Combine like terms: -0.31574268 + -0.2312 = -0.54694268 x = -0.54694268 Simplifying x = -0.54694268Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.08454268, -0.54694268}
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