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Simplifying (4x * 3 + -2x2 + 6) + -1(4x * 3 + 5x * 2 + -12) = 0 Reorder the terms for easier multiplication: (4 * 3x + -2x2 + 6) + -1(4x * 3 + 5x * 2 + -12) = 0 Multiply 4 * 3 (12x + -2x2 + 6) + -1(4x * 3 + 5x * 2 + -12) = 0 Reorder the terms: (6 + 12x + -2x2) + -1(4x * 3 + 5x * 2 + -12) = 0 Remove parenthesis around (6 + 12x + -2x2) 6 + 12x + -2x2 + -1(4x * 3 + 5x * 2 + -12) = 0 Reorder the terms for easier multiplication: 6 + 12x + -2x2 + -1(4 * 3x + 5x * 2 + -12) = 0 Multiply 4 * 3 6 + 12x + -2x2 + -1(12x + 5x * 2 + -12) = 0 Reorder the terms for easier multiplication: 6 + 12x + -2x2 + -1(12x + 5 * 2x + -12) = 0 Multiply 5 * 2 6 + 12x + -2x2 + -1(12x + 10x + -12) = 0 Reorder the terms: 6 + 12x + -2x2 + -1(-12 + 12x + 10x) = 0 Combine like terms: 12x + 10x = 22x 6 + 12x + -2x2 + -1(-12 + 22x) = 0 6 + 12x + -2x2 + (-12 * -1 + 22x * -1) = 0 6 + 12x + -2x2 + (12 + -22x) = 0 Reorder the terms: 6 + 12 + 12x + -22x + -2x2 = 0 Combine like terms: 6 + 12 = 18 18 + 12x + -22x + -2x2 = 0 Combine like terms: 12x + -22x = -10x 18 + -10x + -2x2 = 0 Solving 18 + -10x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 9 + -5x + -1x2 = 0 Solving 9 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5x + x2 = 0 + 9 5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 5x + x2 = 9 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 9 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + 5x + x2 = 15.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 2.5 = 3.905124838 Simplifying x + 2.5 = 3.905124838 Reorder the terms: 2.5 + x = 3.905124838 Solving 2.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.905124838 + -2.5 x = 3.905124838 + -2.5 Combine like terms: 3.905124838 + -2.5 = 1.405124838 x = 1.405124838 Simplifying x = 1.405124838Subproblem 2
x + 2.5 = -3.905124838 Simplifying x + 2.5 = -3.905124838 Reorder the terms: 2.5 + x = -3.905124838 Solving 2.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.905124838 + -2.5 x = -3.905124838 + -2.5 Combine like terms: -3.905124838 + -2.5 = -6.405124838 x = -6.405124838 Simplifying x = -6.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.405124838, -6.405124838}Solution
x = {1.405124838, -6.405124838}
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