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Simplifying -16x2 + 72x + 7 = 0 Reorder the terms: 7 + 72x + -16x2 = 0 Solving 7 + 72x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.4375 + -4.5x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -4.5x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -4.5x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -4.5x + x2 = 0 + 0.4375 -4.5x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -4.5x + x2 = 0.4375 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 0.4375 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 0.4375 + 5.0625 Combine like terms: 0.4375 + 5.0625 = 5.5 5.0625 + -4.5x + x2 = 5.5 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + -2.25) equal to 2.34520788 and -2.34520788.Subproblem 1
x + -2.25 = 2.34520788 Simplifying x + -2.25 = 2.34520788 Reorder the terms: -2.25 + x = 2.34520788 Solving -2.25 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.34520788 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.34520788 + 2.25 x = 2.34520788 + 2.25 Combine like terms: 2.34520788 + 2.25 = 4.59520788 x = 4.59520788 Simplifying x = 4.59520788Subproblem 2
x + -2.25 = -2.34520788 Simplifying x + -2.25 = -2.34520788 Reorder the terms: -2.25 + x = -2.34520788 Solving -2.25 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.34520788 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.34520788 + 2.25 x = -2.34520788 + 2.25 Combine like terms: -2.34520788 + 2.25 = -0.09520788 x = -0.09520788 Simplifying x = -0.09520788Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.59520788, -0.09520788}
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