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Simplifying x = -0.15x2 + 153x + -1500 Reorder the terms: x = -1500 + 153x + -0.15x2 Solving x = -1500 + 153x + -0.15x2 Solving for variable 'x'. Reorder the terms: 1500 + x + -153x + 0.15x2 = -1500 + 153x + -0.15x2 + 1500 + -153x + 0.15x2 Combine like terms: x + -153x = -152x 1500 + -152x + 0.15x2 = -1500 + 153x + -0.15x2 + 1500 + -153x + 0.15x2 Reorder the terms: 1500 + -152x + 0.15x2 = -1500 + 1500 + 153x + -153x + -0.15x2 + 0.15x2 Combine like terms: -1500 + 1500 = 0 1500 + -152x + 0.15x2 = 0 + 153x + -153x + -0.15x2 + 0.15x2 1500 + -152x + 0.15x2 = 153x + -153x + -0.15x2 + 0.15x2 Combine like terms: 153x + -153x = 0 1500 + -152x + 0.15x2 = 0 + -0.15x2 + 0.15x2 1500 + -152x + 0.15x2 = -0.15x2 + 0.15x2 Combine like terms: -0.15x2 + 0.15x2 = 0.00 1500 + -152x + 0.15x2 = 0.00 Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. 10000 + -1013.333333x + x2 = 0 Move the constant term to the right: Add '-10000' to each side of the equation. 10000 + -1013.333333x + -10000 + x2 = 0 + -10000 Reorder the terms: 10000 + -10000 + -1013.333333x + x2 = 0 + -10000 Combine like terms: 10000 + -10000 = 0 0 + -1013.333333x + x2 = 0 + -10000 -1013.333333x + x2 = 0 + -10000 Combine like terms: 0 + -10000 = -10000 -1013.333333x + x2 = -10000 The x term is -1013.333333x. Take half its coefficient (-506.6666665). Square it (256711.1109) and add it to both sides. Add '256711.1109' to each side of the equation. -1013.333333x + 256711.1109 + x2 = -10000 + 256711.1109 Reorder the terms: 256711.1109 + -1013.333333x + x2 = -10000 + 256711.1109 Combine like terms: -10000 + 256711.1109 = 246711.1109 256711.1109 + -1013.333333x + x2 = 246711.1109 Factor a perfect square on the left side: (x + -506.6666665)(x + -506.6666665) = 246711.1109 Calculate the square root of the right side: 496.700222368 Break this problem into two subproblems by setting (x + -506.6666665) equal to 496.700222368 and -496.700222368.Subproblem 1
x + -506.6666665 = 496.700222368 Simplifying x + -506.6666665 = 496.700222368 Reorder the terms: -506.6666665 + x = 496.700222368 Solving -506.6666665 + x = 496.700222368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '506.6666665' to each side of the equation. -506.6666665 + 506.6666665 + x = 496.700222368 + 506.6666665 Combine like terms: -506.6666665 + 506.6666665 = 0.0000000 0.0000000 + x = 496.700222368 + 506.6666665 x = 496.700222368 + 506.6666665 Combine like terms: 496.700222368 + 506.6666665 = 1003.366888868 x = 1003.366888868 Simplifying x = 1003.366888868Subproblem 2
x + -506.6666665 = -496.700222368 Simplifying x + -506.6666665 = -496.700222368 Reorder the terms: -506.6666665 + x = -496.700222368 Solving -506.6666665 + x = -496.700222368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '506.6666665' to each side of the equation. -506.6666665 + 506.6666665 + x = -496.700222368 + 506.6666665 Combine like terms: -506.6666665 + 506.6666665 = 0.0000000 0.0000000 + x = -496.700222368 + 506.6666665 x = -496.700222368 + 506.6666665 Combine like terms: -496.700222368 + 506.6666665 = 9.966444132 x = 9.966444132 Simplifying x = 9.966444132Solution
The solution to the problem is based on the solutions from the subproblems. x = {1003.366888868, 9.966444132}
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