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Simplifying 10 = -16x2 + 50x + 30 Reorder the terms: 10 = 30 + 50x + -16x2 Solving 10 = 30 + 50x + -16x2 Solving for variable 'x'. Combine like terms: 10 + -30 = -20 -20 + -50x + 16x2 = 30 + 50x + -16x2 + -30 + -50x + 16x2 Reorder the terms: -20 + -50x + 16x2 = 30 + -30 + 50x + -50x + -16x2 + 16x2 Combine like terms: 30 + -30 = 0 -20 + -50x + 16x2 = 0 + 50x + -50x + -16x2 + 16x2 -20 + -50x + 16x2 = 50x + -50x + -16x2 + 16x2 Combine like terms: 50x + -50x = 0 -20 + -50x + 16x2 = 0 + -16x2 + 16x2 -20 + -50x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -20 + -50x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -25x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -25x + 8x2)' equal to zero and attempt to solve: Simplifying -10 + -25x + 8x2 = 0 Solving -10 + -25x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + -3.125x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -3.125x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -3.125x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -3.125x + x2 = 0 + 1.25 -3.125x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -3.125x + x2 = 1.25 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 1.25 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 1.25 + 2.44140625 Combine like terms: 1.25 + 2.44140625 = 3.69140625 2.44140625 + -3.125x + x2 = 3.69140625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 3.69140625 Calculate the square root of the right side: 1.921303269 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.921303269 and -1.921303269.Subproblem 1
x + -1.5625 = 1.921303269 Simplifying x + -1.5625 = 1.921303269 Reorder the terms: -1.5625 + x = 1.921303269 Solving -1.5625 + x = 1.921303269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.921303269 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.921303269 + 1.5625 x = 1.921303269 + 1.5625 Combine like terms: 1.921303269 + 1.5625 = 3.483803269 x = 3.483803269 Simplifying x = 3.483803269Subproblem 2
x + -1.5625 = -1.921303269 Simplifying x + -1.5625 = -1.921303269 Reorder the terms: -1.5625 + x = -1.921303269 Solving -1.5625 + x = -1.921303269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.921303269 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.921303269 + 1.5625 x = -1.921303269 + 1.5625 Combine like terms: -1.921303269 + 1.5625 = -0.358803269 x = -0.358803269 Simplifying x = -0.358803269Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.483803269, -0.358803269}Solution
x = {3.483803269, -0.358803269}
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