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Simplifying 4900 = (x + -3)(x) Reorder the terms: 4900 = (-3 + x)(x) Reorder the terms for easier multiplication: 4900 = x(-3 + x) 4900 = (-3 * x + x * x) 4900 = (-3x + x2) Solving 4900 = -3x + x2 Solving for variable 'x'. Reorder the terms: 4900 + 3x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 4900 + 3x + -1x2 = 0 + x2 + -1x2 4900 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4900 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4900 + -3x + x2 = 0 Move the constant term to the right: Add '4900' to each side of the equation. -4900 + -3x + 4900 + x2 = 0 + 4900 Reorder the terms: -4900 + 4900 + -3x + x2 = 0 + 4900 Combine like terms: -4900 + 4900 = 0 0 + -3x + x2 = 0 + 4900 -3x + x2 = 0 + 4900 Combine like terms: 0 + 4900 = 4900 -3x + x2 = 4900 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 4900 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 4900 + 2.25 Combine like terms: 4900 + 2.25 = 4902.25 2.25 + -3x + x2 = 4902.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4902.25 Calculate the square root of the right side: 70.016069584 Break this problem into two subproblems by setting (x + -1.5) equal to 70.016069584 and -70.016069584.Subproblem 1
x + -1.5 = 70.016069584 Simplifying x + -1.5 = 70.016069584 Reorder the terms: -1.5 + x = 70.016069584 Solving -1.5 + x = 70.016069584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 70.016069584 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 70.016069584 + 1.5 x = 70.016069584 + 1.5 Combine like terms: 70.016069584 + 1.5 = 71.516069584 x = 71.516069584 Simplifying x = 71.516069584Subproblem 2
x + -1.5 = -70.016069584 Simplifying x + -1.5 = -70.016069584 Reorder the terms: -1.5 + x = -70.016069584 Solving -1.5 + x = -70.016069584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -70.016069584 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -70.016069584 + 1.5 x = -70.016069584 + 1.5 Combine like terms: -70.016069584 + 1.5 = -68.516069584 x = -68.516069584 Simplifying x = -68.516069584Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.516069584, -68.516069584}
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