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Simplifying 2x2 + 28x = 78 Reorder the terms: 28x + 2x2 = 78 Solving 28x + 2x2 = 78 Solving for variable 'x'. Reorder the terms: -78 + 28x + 2x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -78 + 28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-39 + 14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-39 + 14x + x2)' equal to zero and attempt to solve: Simplifying -39 + 14x + x2 = 0 Solving -39 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 14x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 14x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 14x + x2 = 0 + 39 14x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 14x + x2 = 39 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 39 + 49 Reorder the terms: 49 + 14x + x2 = 39 + 49 Combine like terms: 39 + 49 = 88 49 + 14x + x2 = 88 Factor a perfect square on the left side: (x + 7)(x + 7) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + 7) equal to 9.38083152 and -9.38083152.Subproblem 1
x + 7 = 9.38083152 Simplifying x + 7 = 9.38083152 Reorder the terms: 7 + x = 9.38083152 Solving 7 + x = 9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 9.38083152 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.38083152 + -7 x = 9.38083152 + -7 Combine like terms: 9.38083152 + -7 = 2.38083152 x = 2.38083152 Simplifying x = 2.38083152Subproblem 2
x + 7 = -9.38083152 Simplifying x + 7 = -9.38083152 Reorder the terms: 7 + x = -9.38083152 Solving 7 + x = -9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -9.38083152 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.38083152 + -7 x = -9.38083152 + -7 Combine like terms: -9.38083152 + -7 = -16.38083152 x = -16.38083152 Simplifying x = -16.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.38083152, -16.38083152}Solution
x = {2.38083152, -16.38083152}
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