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Simplifying 0 = 30 + 70X + -16X2 Solving 0 = 30 + 70X + -16X2 Solving for variable 'X'. Combine like terms: 0 + -30 = -30 -30 + -70X + 16X2 = 30 + 70X + -16X2 + -30 + -70X + 16X2 Reorder the terms: -30 + -70X + 16X2 = 30 + -30 + 70X + -70X + -16X2 + 16X2 Combine like terms: 30 + -30 = 0 -30 + -70X + 16X2 = 0 + 70X + -70X + -16X2 + 16X2 -30 + -70X + 16X2 = 70X + -70X + -16X2 + 16X2 Combine like terms: 70X + -70X = 0 -30 + -70X + 16X2 = 0 + -16X2 + 16X2 -30 + -70X + 16X2 = -16X2 + 16X2 Combine like terms: -16X2 + 16X2 = 0 -30 + -70X + 16X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -35X + 8X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -35X + 8X2)' equal to zero and attempt to solve: Simplifying -15 + -35X + 8X2 = 0 Solving -15 + -35X + 8X2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -4.375X + X2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -4.375X + 1.875 + X2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -4.375X + X2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -4.375X + X2 = 0 + 1.875 -4.375X + X2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -4.375X + X2 = 1.875 The X term is -4.375X. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375X + 4.78515625 + X2 = 1.875 + 4.78515625 Reorder the terms: 4.78515625 + -4.375X + X2 = 1.875 + 4.78515625 Combine like terms: 1.875 + 4.78515625 = 6.66015625 4.78515625 + -4.375X + X2 = 6.66015625 Factor a perfect square on the left side: (X + -2.1875)(X + -2.1875) = 6.66015625 Calculate the square root of the right side: 2.580727853 Break this problem into two subproblems by setting (X + -2.1875) equal to 2.580727853 and -2.580727853.Subproblem 1
X + -2.1875 = 2.580727853 Simplifying X + -2.1875 = 2.580727853 Reorder the terms: -2.1875 + X = 2.580727853 Solving -2.1875 + X = 2.580727853 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + X = 2.580727853 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + X = 2.580727853 + 2.1875 X = 2.580727853 + 2.1875 Combine like terms: 2.580727853 + 2.1875 = 4.768227853 X = 4.768227853 Simplifying X = 4.768227853Subproblem 2
X + -2.1875 = -2.580727853 Simplifying X + -2.1875 = -2.580727853 Reorder the terms: -2.1875 + X = -2.580727853 Solving -2.1875 + X = -2.580727853 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + X = -2.580727853 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + X = -2.580727853 + 2.1875 X = -2.580727853 + 2.1875 Combine like terms: -2.580727853 + 2.1875 = -0.393227853 X = -0.393227853 Simplifying X = -0.393227853Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.768227853, -0.393227853}Solution
X = {4.768227853, -0.393227853}
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