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Simplifying 16x2 + -72x = 15 Reorder the terms: -72x + 16x2 = 15 Solving -72x + 16x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -72x + 16x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -72x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -4.5x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -4.5x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -4.5x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -4.5x + x2 = 0 + 0.9375 -4.5x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -4.5x + x2 = 0.9375 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 = 0.9375 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 0.9375 + 5.0625 Combine like terms: 0.9375 + 5.0625 = 6 5.0625 + -4.5x + x2 = 6 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -2.25) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -2.25 = 2.449489743 Simplifying x + -2.25 = 2.449489743 Reorder the terms: -2.25 + x = 2.449489743 Solving -2.25 + x = 2.449489743 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 = 2.449489743 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.449489743 + 2.25 x = 2.449489743 + 2.25 Combine like terms: 2.449489743 + 2.25 = 4.699489743 x = 4.699489743 Simplifying x = 4.699489743Subproblem 2
x + -2.25 = -2.449489743 Simplifying x + -2.25 = -2.449489743 Reorder the terms: -2.25 + x = -2.449489743 Solving -2.25 + x = -2.449489743 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 = -2.449489743 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.449489743 + 2.25 x = -2.449489743 + 2.25 Combine like terms: -2.449489743 + 2.25 = -0.199489743 x = -0.199489743 Simplifying x = -0.199489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.699489743, -0.199489743}
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