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Simplifying 28x + 12x2 = 126 Solving 28x + 12x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + 28x + 12x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 28x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-63 + 14x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-63 + 14x + 6x2)' equal to zero and attempt to solve: Simplifying -63 + 14x + 6x2 = 0 Solving -63 + 14x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.5 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 2.333333333x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 2.333333333x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 2.333333333x + x2 = 0 + 10.5 2.333333333x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 2.333333333x + x2 = 10.5 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 10.5 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 10.5 + 1.361111112 Combine like terms: 10.5 + 1.361111112 = 11.861111112 1.361111112 + 2.333333333x + x2 = 11.861111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 11.861111112 Calculate the square root of the right side: 3.443996387 Break this problem into two subproblems by setting (x + 1.166666667) equal to 3.443996387 and -3.443996387.Subproblem 1
x + 1.166666667 = 3.443996387 Simplifying x + 1.166666667 = 3.443996387 Reorder the terms: 1.166666667 + x = 3.443996387 Solving 1.166666667 + x = 3.443996387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 3.443996387 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 3.443996387 + -1.166666667 x = 3.443996387 + -1.166666667 Combine like terms: 3.443996387 + -1.166666667 = 2.27732972 x = 2.27732972 Simplifying x = 2.27732972Subproblem 2
x + 1.166666667 = -3.443996387 Simplifying x + 1.166666667 = -3.443996387 Reorder the terms: 1.166666667 + x = -3.443996387 Solving 1.166666667 + x = -3.443996387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -3.443996387 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -3.443996387 + -1.166666667 x = -3.443996387 + -1.166666667 Combine like terms: -3.443996387 + -1.166666667 = -4.610663054 x = -4.610663054 Simplifying x = -4.610663054Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.27732972, -4.610663054}Solution
x = {2.27732972, -4.610663054}
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