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Simplifying 6x2 + 15x + -84 = 0 Reorder the terms: -84 + 15x + 6x2 = 0 Solving -84 + 15x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + 5x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-28 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -28 + 5x + 2x2 = 0 Solving -28 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 2.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 2.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 2.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2.5x + x2 = 0 + 14 2.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 2.5x + x2 = 14 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 14 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 14 + 1.5625 Combine like terms: 14 + 1.5625 = 15.5625 1.5625 + 2.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + 1.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + 1.25 = 3.94493346 Simplifying x + 1.25 = 3.94493346 Reorder the terms: 1.25 + x = 3.94493346 Solving 1.25 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.94493346 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.94493346 + -1.25 x = 3.94493346 + -1.25 Combine like terms: 3.94493346 + -1.25 = 2.69493346 x = 2.69493346 Simplifying x = 2.69493346Subproblem 2
x + 1.25 = -3.94493346 Simplifying x + 1.25 = -3.94493346 Reorder the terms: 1.25 + x = -3.94493346 Solving 1.25 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.94493346 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.94493346 + -1.25 x = -3.94493346 + -1.25 Combine like terms: -3.94493346 + -1.25 = -5.19493346 x = -5.19493346 Simplifying x = -5.19493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.69493346, -5.19493346}Solution
x = {2.69493346, -5.19493346}
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