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Simplifying -16x2 + 1000x = 1150 Reorder the terms: 1000x + -16x2 = 1150 Solving 1000x + -16x2 = 1150 Solving for variable 'x'. Reorder the terms: -1150 + 1000x + -16x2 = 1150 + -1150 Combine like terms: 1150 + -1150 = 0 -1150 + 1000x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-575 + 500x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-575 + 500x + -8x2)' equal to zero and attempt to solve: Simplifying -575 + 500x + -8x2 = 0 Solving -575 + 500x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 71.875 + -62.5x + x2 = 0 Move the constant term to the right: Add '-71.875' to each side of the equation. 71.875 + -62.5x + -71.875 + x2 = 0 + -71.875 Reorder the terms: 71.875 + -71.875 + -62.5x + x2 = 0 + -71.875 Combine like terms: 71.875 + -71.875 = 0.000 0.000 + -62.5x + x2 = 0 + -71.875 -62.5x + x2 = 0 + -71.875 Combine like terms: 0 + -71.875 = -71.875 -62.5x + x2 = -71.875 The x term is -62.5x. Take half its coefficient (-31.25). Square it (976.5625) and add it to both sides. Add '976.5625' to each side of the equation. -62.5x + 976.5625 + x2 = -71.875 + 976.5625 Reorder the terms: 976.5625 + -62.5x + x2 = -71.875 + 976.5625 Combine like terms: -71.875 + 976.5625 = 904.6875 976.5625 + -62.5x + x2 = 904.6875 Factor a perfect square on the left side: (x + -31.25)(x + -31.25) = 904.6875 Calculate the square root of the right side: 30.078023539 Break this problem into two subproblems by setting (x + -31.25) equal to 30.078023539 and -30.078023539.Subproblem 1
x + -31.25 = 30.078023539 Simplifying x + -31.25 = 30.078023539 Reorder the terms: -31.25 + x = 30.078023539 Solving -31.25 + x = 30.078023539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.25' to each side of the equation. -31.25 + 31.25 + x = 30.078023539 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + x = 30.078023539 + 31.25 x = 30.078023539 + 31.25 Combine like terms: 30.078023539 + 31.25 = 61.328023539 x = 61.328023539 Simplifying x = 61.328023539Subproblem 2
x + -31.25 = -30.078023539 Simplifying x + -31.25 = -30.078023539 Reorder the terms: -31.25 + x = -30.078023539 Solving -31.25 + x = -30.078023539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.25' to each side of the equation. -31.25 + 31.25 + x = -30.078023539 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + x = -30.078023539 + 31.25 x = -30.078023539 + 31.25 Combine like terms: -30.078023539 + 31.25 = 1.171976461 x = 1.171976461 Simplifying x = 1.171976461Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.328023539, 1.171976461}Solution
x = {61.328023539, 1.171976461}
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