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Simplifying -28x(4x + 14) + 16 = -28x + 128 Reorder the terms: -28x(14 + 4x) + 16 = -28x + 128 (14 * -28x + 4x * -28x) + 16 = -28x + 128 (-392x + -112x2) + 16 = -28x + 128 Reorder the terms: 16 + -392x + -112x2 = -28x + 128 Reorder the terms: 16 + -392x + -112x2 = 128 + -28x Solving 16 + -392x + -112x2 = 128 + -28x Solving for variable 'x'. Reorder the terms: 16 + -128 + -392x + 28x + -112x2 = 128 + -28x + -128 + 28x Combine like terms: 16 + -128 = -112 -112 + -392x + 28x + -112x2 = 128 + -28x + -128 + 28x Combine like terms: -392x + 28x = -364x -112 + -364x + -112x2 = 128 + -28x + -128 + 28x Reorder the terms: -112 + -364x + -112x2 = 128 + -128 + -28x + 28x Combine like terms: 128 + -128 = 0 -112 + -364x + -112x2 = 0 + -28x + 28x -112 + -364x + -112x2 = -28x + 28x Combine like terms: -28x + 28x = 0 -112 + -364x + -112x2 = 0 Factor out the Greatest Common Factor (GCF), '-28'. -28(4 + 13x + 4x2) = 0 Ignore the factor -28.Subproblem 1
Set the factor '(4 + 13x + 4x2)' equal to zero and attempt to solve: Simplifying 4 + 13x + 4x2 = 0 Solving 4 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 3.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.25x + x2 = 0 + -1 3.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.25x + x2 = -1 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = -1 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = -1 + 2.640625 Combine like terms: -1 + 2.640625 = 1.640625 2.640625 + 3.25x + x2 = 1.640625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 1.625) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 1.625 = 1.280868846 Simplifying x + 1.625 = 1.280868846 Reorder the terms: 1.625 + x = 1.280868846 Solving 1.625 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 1.280868846 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.280868846 + -1.625 x = 1.280868846 + -1.625 Combine like terms: 1.280868846 + -1.625 = -0.344131154 x = -0.344131154 Simplifying x = -0.344131154Subproblem 2
x + 1.625 = -1.280868846 Simplifying x + 1.625 = -1.280868846 Reorder the terms: 1.625 + x = -1.280868846 Solving 1.625 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -1.280868846 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.280868846 + -1.625 x = -1.280868846 + -1.625 Combine like terms: -1.280868846 + -1.625 = -2.905868846 x = -2.905868846 Simplifying x = -2.905868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.344131154, -2.905868846}Solution
x = {-0.344131154, -2.905868846}
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