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Simplifying 6x2 + 12x + -89 = 5 Reorder the terms: -89 + 12x + 6x2 = 5 Solving -89 + 12x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: -89 + -5 + 12x + 6x2 = 5 + -5 Combine like terms: -89 + -5 = -94 -94 + 12x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -94 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying -47 + 6x + 3x2 = 0 Solving -47 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15.66666667 + 2x + x2 = 0 Move the constant term to the right: Add '15.66666667' to each side of the equation. -15.66666667 + 2x + 15.66666667 + x2 = 0 + 15.66666667 Reorder the terms: -15.66666667 + 15.66666667 + 2x + x2 = 0 + 15.66666667 Combine like terms: -15.66666667 + 15.66666667 = 0.00000000 0.00000000 + 2x + x2 = 0 + 15.66666667 2x + x2 = 0 + 15.66666667 Combine like terms: 0 + 15.66666667 = 15.66666667 2x + x2 = 15.66666667 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 15.66666667 + 1 Reorder the terms: 1 + 2x + x2 = 15.66666667 + 1 Combine like terms: 15.66666667 + 1 = 16.66666667 1 + 2x + x2 = 16.66666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 16.66666667 Calculate the square root of the right side: 4.082482905 Break this problem into two subproblems by setting (x + 1) equal to 4.082482905 and -4.082482905.Subproblem 1
x + 1 = 4.082482905 Simplifying x + 1 = 4.082482905 Reorder the terms: 1 + x = 4.082482905 Solving 1 + x = 4.082482905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.082482905 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.082482905 + -1 x = 4.082482905 + -1 Combine like terms: 4.082482905 + -1 = 3.082482905 x = 3.082482905 Simplifying x = 3.082482905Subproblem 2
x + 1 = -4.082482905 Simplifying x + 1 = -4.082482905 Reorder the terms: 1 + x = -4.082482905 Solving 1 + x = -4.082482905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.082482905 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.082482905 + -1 x = -4.082482905 + -1 Combine like terms: -4.082482905 + -1 = -5.082482905 x = -5.082482905 Simplifying x = -5.082482905Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.082482905, -5.082482905}Solution
x = {3.082482905, -5.082482905}
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