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Simplifying -16x2 + 144x + 7 = 0 Reorder the terms: 7 + 144x + -16x2 = 0 Solving 7 + 144x + -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 + -9x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -9x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -9x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -9x + x2 = 0 + 0.4375 -9x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -9x + x2 = 0.4375 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 0.4375 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 0.4375 + 20.25 Combine like terms: 0.4375 + 20.25 = 20.6875 20.25 + -9x + x2 = 20.6875 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 20.6875 Calculate the square root of the right side: 4.54835135 Break this problem into two subproblems by setting (x + -4.5) equal to 4.54835135 and -4.54835135.Subproblem 1
x + -4.5 = 4.54835135 Simplifying x + -4.5 = 4.54835135 Reorder the terms: -4.5 + x = 4.54835135 Solving -4.5 + x = 4.54835135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.54835135 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.54835135 + 4.5 x = 4.54835135 + 4.5 Combine like terms: 4.54835135 + 4.5 = 9.04835135 x = 9.04835135 Simplifying x = 9.04835135Subproblem 2
x + -4.5 = -4.54835135 Simplifying x + -4.5 = -4.54835135 Reorder the terms: -4.5 + x = -4.54835135 Solving -4.5 + x = -4.54835135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.54835135 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.54835135 + 4.5 x = -4.54835135 + 4.5 Combine like terms: -4.54835135 + 4.5 = -0.04835135 x = -0.04835135 Simplifying x = -0.04835135Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.04835135, -0.04835135}
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