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Simplifying 0.02x2 + 50 = 200 + -3x Reorder the terms: 50 + 0.02x2 = 200 + -3x Solving 50 + 0.02x2 = 200 + -3x Solving for variable 'x'. Reorder the terms: 50 + -200 + 3x + 0.02x2 = 200 + -3x + -200 + 3x Combine like terms: 50 + -200 = -150 -150 + 3x + 0.02x2 = 200 + -3x + -200 + 3x Reorder the terms: -150 + 3x + 0.02x2 = 200 + -200 + -3x + 3x Combine like terms: 200 + -200 = 0 -150 + 3x + 0.02x2 = 0 + -3x + 3x -150 + 3x + 0.02x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -150 + 3x + 0.02x2 = 0 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -7500 + 150x + x2 = 0 Move the constant term to the right: Add '7500' to each side of the equation. -7500 + 150x + 7500 + x2 = 0 + 7500 Reorder the terms: -7500 + 7500 + 150x + x2 = 0 + 7500 Combine like terms: -7500 + 7500 = 0 0 + 150x + x2 = 0 + 7500 150x + x2 = 0 + 7500 Combine like terms: 0 + 7500 = 7500 150x + x2 = 7500 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 = 7500 + 5625 Reorder the terms: 5625 + 150x + x2 = 7500 + 5625 Combine like terms: 7500 + 5625 = 13125 5625 + 150x + x2 = 13125 Factor a perfect square on the left side: (x + 75)(x + 75) = 13125 Calculate the square root of the right side: 114.564392374 Break this problem into two subproblems by setting (x + 75) equal to 114.564392374 and -114.564392374.Subproblem 1
x + 75 = 114.564392374 Simplifying x + 75 = 114.564392374 Reorder the terms: 75 + x = 114.564392374 Solving 75 + x = 114.564392374 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 = 114.564392374 + -75 Combine like terms: 75 + -75 = 0 0 + x = 114.564392374 + -75 x = 114.564392374 + -75 Combine like terms: 114.564392374 + -75 = 39.564392374 x = 39.564392374 Simplifying x = 39.564392374Subproblem 2
x + 75 = -114.564392374 Simplifying x + 75 = -114.564392374 Reorder the terms: 75 + x = -114.564392374 Solving 75 + x = -114.564392374 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 = -114.564392374 + -75 Combine like terms: 75 + -75 = 0 0 + x = -114.564392374 + -75 x = -114.564392374 + -75 Combine like terms: -114.564392374 + -75 = -189.564392374 x = -189.564392374 Simplifying x = -189.564392374Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.564392374, -189.564392374}
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