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Simplifying -4x(6 + -1x) = 7 (6 * -4x + -1x * -4x) = 7 (-24x + 4x2) = 7 Solving -24x + 4x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -24x + 4x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -6x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -6x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -6x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -6x + x2 = 0 + 1.75 -6x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -6x + x2 = 1.75 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1.75 + 9 Reorder the terms: 9 + -6x + x2 = 1.75 + 9 Combine like terms: 1.75 + 9 = 10.75 9 + -6x + x2 = 10.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x + -3) equal to 3.278719262 and -3.278719262.Subproblem 1
x + -3 = 3.278719262 Simplifying x + -3 = 3.278719262 Reorder the terms: -3 + x = 3.278719262 Solving -3 + x = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.278719262 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.278719262 + 3 x = 3.278719262 + 3 Combine like terms: 3.278719262 + 3 = 6.278719262 x = 6.278719262 Simplifying x = 6.278719262Subproblem 2
x + -3 = -3.278719262 Simplifying x + -3 = -3.278719262 Reorder the terms: -3 + x = -3.278719262 Solving -3 + x = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.278719262 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.278719262 + 3 x = -3.278719262 + 3 Combine like terms: -3.278719262 + 3 = -0.278719262 x = -0.278719262 Simplifying x = -0.278719262Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.278719262, -0.278719262}
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