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Simplifying -16x2 + 100x = 6 Reorder the terms: 100x + -16x2 = 6 Solving 100x + -16x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 100x + -16x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 100x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 50x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 50x + -8x2)' equal to zero and attempt to solve: Simplifying -3 + 50x + -8x2 = 0 Solving -3 + 50x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.375 + -6.25x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -6.25x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -6.25x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -6.25x + x2 = 0 + -0.375 -6.25x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -6.25x + x2 = -0.375 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -0.375 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -0.375 + 9.765625 Combine like terms: -0.375 + 9.765625 = 9.390625 9.765625 + -6.25x + x2 = 9.390625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 9.390625 Calculate the square root of the right side: 3.064412668 Break this problem into two subproblems by setting (x + -3.125) equal to 3.064412668 and -3.064412668.Subproblem 1
x + -3.125 = 3.064412668 Simplifying x + -3.125 = 3.064412668 Reorder the terms: -3.125 + x = 3.064412668 Solving -3.125 + x = 3.064412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.064412668 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.064412668 + 3.125 x = 3.064412668 + 3.125 Combine like terms: 3.064412668 + 3.125 = 6.189412668 x = 6.189412668 Simplifying x = 6.189412668Subproblem 2
x + -3.125 = -3.064412668 Simplifying x + -3.125 = -3.064412668 Reorder the terms: -3.125 + x = -3.064412668 Solving -3.125 + x = -3.064412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.064412668 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.064412668 + 3.125 x = -3.064412668 + 3.125 Combine like terms: -3.064412668 + 3.125 = 0.060587332 x = 0.060587332 Simplifying x = 0.060587332Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.189412668, 0.060587332}Solution
x = {6.189412668, 0.060587332}
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