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Simplifying (4x2 + -7x + -28) + (8x2 + 9x) = 0 Reorder the terms: (-28 + -7x + 4x2) + (8x2 + 9x) = 0 Remove parenthesis around (-28 + -7x + 4x2) -28 + -7x + 4x2 + (8x2 + 9x) = 0 Reorder the terms: -28 + -7x + 4x2 + (9x + 8x2) = 0 Remove parenthesis around (9x + 8x2) -28 + -7x + 4x2 + 9x + 8x2 = 0 Reorder the terms: -28 + -7x + 9x + 4x2 + 8x2 = 0 Combine like terms: -7x + 9x = 2x -28 + 2x + 4x2 + 8x2 = 0 Combine like terms: 4x2 + 8x2 = 12x2 -28 + 2x + 12x2 = 0 Solving -28 + 2x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + x + 6x2)' equal to zero and attempt to solve: Simplifying -14 + x + 6x2 = 0 Solving -14 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.333333333 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 0.1666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 0.1666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 0.1666666667x + x2 = 0 + 2.333333333 0.1666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 0.1666666667x + x2 = 2.333333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667x + 0.25 + x2 = 2.333333333 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = 2.333333333 + 0.25 Combine like terms: 2.333333333 + 0.25 = 2.583333333 0.25 + 0.1666666667x + x2 = 2.583333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.583333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (x + 0.5) equal to 1.607275127 and -1.607275127.Subproblem 1
x + 0.5 = 1.607275127 Simplifying x + 0.5 = 1.607275127 Reorder the terms: 0.5 + x = 1.607275127 Solving 0.5 + x = 1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.607275127 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.607275127 + -0.5 x = 1.607275127 + -0.5 Combine like terms: 1.607275127 + -0.5 = 1.107275127 x = 1.107275127 Simplifying x = 1.107275127Subproblem 2
x + 0.5 = -1.607275127 Simplifying x + 0.5 = -1.607275127 Reorder the terms: 0.5 + x = -1.607275127 Solving 0.5 + x = -1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.607275127 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.607275127 + -0.5 x = -1.607275127 + -0.5 Combine like terms: -1.607275127 + -0.5 = -2.107275127 x = -2.107275127 Simplifying x = -2.107275127Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.107275127, -2.107275127}Solution
x = {1.107275127, -2.107275127}
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