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Simplifying 2 + -0.04x = 70 + 2x + -0.02x2 Solving 2 + -0.04x = 70 + 2x + -0.02x2 Solving for variable 'x'. Reorder the terms: 2 + -70 + -0.04x + -2x + 0.02x2 = 70 + 2x + -0.02x2 + -70 + -2x + 0.02x2 Combine like terms: 2 + -70 = -68 -68 + -0.04x + -2x + 0.02x2 = 70 + 2x + -0.02x2 + -70 + -2x + 0.02x2 Combine like terms: -0.04x + -2x = -2.04x -68 + -2.04x + 0.02x2 = 70 + 2x + -0.02x2 + -70 + -2x + 0.02x2 Reorder the terms: -68 + -2.04x + 0.02x2 = 70 + -70 + 2x + -2x + -0.02x2 + 0.02x2 Combine like terms: 70 + -70 = 0 -68 + -2.04x + 0.02x2 = 0 + 2x + -2x + -0.02x2 + 0.02x2 -68 + -2.04x + 0.02x2 = 2x + -2x + -0.02x2 + 0.02x2 Combine like terms: 2x + -2x = 0 -68 + -2.04x + 0.02x2 = 0 + -0.02x2 + 0.02x2 -68 + -2.04x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 -68 + -2.04x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -3400 + -102x + x2 = 0 Move the constant term to the right: Add '3400' to each side of the equation. -3400 + -102x + 3400 + x2 = 0 + 3400 Reorder the terms: -3400 + 3400 + -102x + x2 = 0 + 3400 Combine like terms: -3400 + 3400 = 0 0 + -102x + x2 = 0 + 3400 -102x + x2 = 0 + 3400 Combine like terms: 0 + 3400 = 3400 -102x + x2 = 3400 The x term is -102x. Take half its coefficient (-51). Square it (2601) and add it to both sides. Add '2601' to each side of the equation. -102x + 2601 + x2 = 3400 + 2601 Reorder the terms: 2601 + -102x + x2 = 3400 + 2601 Combine like terms: 3400 + 2601 = 6001 2601 + -102x + x2 = 6001 Factor a perfect square on the left side: (x + -51)(x + -51) = 6001 Calculate the square root of the right side: 77.466121627 Break this problem into two subproblems by setting (x + -51) equal to 77.466121627 and -77.466121627.Subproblem 1
x + -51 = 77.466121627 Simplifying x + -51 = 77.466121627 Reorder the terms: -51 + x = 77.466121627 Solving -51 + x = 77.466121627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + x = 77.466121627 + 51 Combine like terms: -51 + 51 = 0 0 + x = 77.466121627 + 51 x = 77.466121627 + 51 Combine like terms: 77.466121627 + 51 = 128.466121627 x = 128.466121627 Simplifying x = 128.466121627Subproblem 2
x + -51 = -77.466121627 Simplifying x + -51 = -77.466121627 Reorder the terms: -51 + x = -77.466121627 Solving -51 + x = -77.466121627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + x = -77.466121627 + 51 Combine like terms: -51 + 51 = 0 0 + x = -77.466121627 + 51 x = -77.466121627 + 51 Combine like terms: -77.466121627 + 51 = -26.466121627 x = -26.466121627 Simplifying x = -26.466121627Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.466121627, -26.466121627}
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