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Simplifying x2 + -6x + 72 + 4x2 + -144 = 0 Reorder the terms: 72 + -144 + -6x + x2 + 4x2 = 0 Combine like terms: 72 + -144 = -72 -72 + -6x + x2 + 4x2 = 0 Combine like terms: x2 + 4x2 = 5x2 -72 + -6x + 5x2 = 0 Solving -72 + -6x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.4 + -1.2x + x2 = 0 Move the constant term to the right: Add '14.4' to each side of the equation. -14.4 + -1.2x + 14.4 + x2 = 0 + 14.4 Reorder the terms: -14.4 + 14.4 + -1.2x + x2 = 0 + 14.4 Combine like terms: -14.4 + 14.4 = 0.0 0.0 + -1.2x + x2 = 0 + 14.4 -1.2x + x2 = 0 + 14.4 Combine like terms: 0 + 14.4 = 14.4 -1.2x + x2 = 14.4 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 14.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 14.4 + 0.36 Combine like terms: 14.4 + 0.36 = 14.76 0.36 + -1.2x + x2 = 14.76 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 14.76 Calculate the square root of the right side: 3.841874542 Break this problem into two subproblems by setting (x + -0.6) equal to 3.841874542 and -3.841874542.Subproblem 1
x + -0.6 = 3.841874542 Simplifying x + -0.6 = 3.841874542 Reorder the terms: -0.6 + x = 3.841874542 Solving -0.6 + x = 3.841874542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 3.841874542 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 3.841874542 + 0.6 x = 3.841874542 + 0.6 Combine like terms: 3.841874542 + 0.6 = 4.441874542 x = 4.441874542 Simplifying x = 4.441874542Subproblem 2
x + -0.6 = -3.841874542 Simplifying x + -0.6 = -3.841874542 Reorder the terms: -0.6 + x = -3.841874542 Solving -0.6 + x = -3.841874542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -3.841874542 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -3.841874542 + 0.6 x = -3.841874542 + 0.6 Combine like terms: -3.841874542 + 0.6 = -3.241874542 x = -3.241874542 Simplifying x = -3.241874542Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.441874542, -3.241874542}
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