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Simplifying 0 = 15x + -0.1x2 + -260 Reorder the terms: 0 = -260 + 15x + -0.1x2 Solving 0 = -260 + 15x + -0.1x2 Solving for variable 'x'. Combine like terms: 0 + 260 = 260 260 + -15x + 0.1x2 = -260 + 15x + -0.1x2 + 260 + -15x + 0.1x2 Reorder the terms: 260 + -15x + 0.1x2 = -260 + 260 + 15x + -15x + -0.1x2 + 0.1x2 Combine like terms: -260 + 260 = 0 260 + -15x + 0.1x2 = 0 + 15x + -15x + -0.1x2 + 0.1x2 260 + -15x + 0.1x2 = 15x + -15x + -0.1x2 + 0.1x2 Combine like terms: 15x + -15x = 0 260 + -15x + 0.1x2 = 0 + -0.1x2 + 0.1x2 260 + -15x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 260 + -15x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 2600 + -150x + x2 = 0 Move the constant term to the right: Add '-2600' to each side of the equation. 2600 + -150x + -2600 + x2 = 0 + -2600 Reorder the terms: 2600 + -2600 + -150x + x2 = 0 + -2600 Combine like terms: 2600 + -2600 = 0 0 + -150x + x2 = 0 + -2600 -150x + x2 = 0 + -2600 Combine like terms: 0 + -2600 = -2600 -150x + x2 = -2600 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = -2600 + 5625 Reorder the terms: 5625 + -150x + x2 = -2600 + 5625 Combine like terms: -2600 + 5625 = 3025 5625 + -150x + x2 = 3025 Factor a perfect square on the left side: (x + -75)(x + -75) = 3025 Calculate the square root of the right side: 55 Break this problem into two subproblems by setting (x + -75) equal to 55 and -55.Subproblem 1
x + -75 = 55 Simplifying x + -75 = 55 Reorder the terms: -75 + x = 55 Solving -75 + x = 55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 55 + 75 Combine like terms: -75 + 75 = 0 0 + x = 55 + 75 x = 55 + 75 Combine like terms: 55 + 75 = 130 x = 130 Simplifying x = 130Subproblem 2
x + -75 = -55 Simplifying x + -75 = -55 Reorder the terms: -75 + x = -55 Solving -75 + x = -55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -55 + 75 Combine like terms: -75 + 75 = 0 0 + x = -55 + 75 x = -55 + 75 Combine like terms: -55 + 75 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {130, 20}
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