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Simplifying -16x2 + 80x + 4 = 10 Reorder the terms: 4 + 80x + -16x2 = 10 Solving 4 + 80x + -16x2 = 10 Solving for variable 'x'. Reorder the terms: 4 + -10 + 80x + -16x2 = 10 + -10 Combine like terms: 4 + -10 = -6 -6 + 80x + -16x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -6 + 80x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 40x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 40x + -8x2)' equal to zero and attempt to solve: Simplifying -3 + 40x + -8x2 = 0 Solving -3 + 40x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.375 + -5x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -5x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -5x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -5x + x2 = 0 + -0.375 -5x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -5x + x2 = -0.375 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.375 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.375 + 6.25 Combine like terms: -0.375 + 6.25 = 5.875 6.25 + -5x + x2 = 5.875 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.875 Calculate the square root of the right side: 2.423839929 Break this problem into two subproblems by setting (x + -2.5) equal to 2.423839929 and -2.423839929.Subproblem 1
x + -2.5 = 2.423839929 Simplifying x + -2.5 = 2.423839929 Reorder the terms: -2.5 + x = 2.423839929 Solving -2.5 + x = 2.423839929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.423839929 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.423839929 + 2.5 x = 2.423839929 + 2.5 Combine like terms: 2.423839929 + 2.5 = 4.923839929 x = 4.923839929 Simplifying x = 4.923839929Subproblem 2
x + -2.5 = -2.423839929 Simplifying x + -2.5 = -2.423839929 Reorder the terms: -2.5 + x = -2.423839929 Solving -2.5 + x = -2.423839929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.423839929 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.423839929 + 2.5 x = -2.423839929 + 2.5 Combine like terms: -2.423839929 + 2.5 = 0.076160071 x = 0.076160071 Simplifying x = 0.076160071Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.923839929, 0.076160071}Solution
x = {4.923839929, 0.076160071}
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