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Simplifying 0 = 4 + (3x + -6)(x + 7) Reorder the terms: 0 = 4 + (-6 + 3x)(x + 7) Reorder the terms: 0 = 4 + (-6 + 3x)(7 + x) Multiply (-6 + 3x) * (7 + x) 0 = 4 + (-6(7 + x) + 3x * (7 + x)) 0 = 4 + ((7 * -6 + x * -6) + 3x * (7 + x)) 0 = 4 + ((-42 + -6x) + 3x * (7 + x)) 0 = 4 + (-42 + -6x + (7 * 3x + x * 3x)) 0 = 4 + (-42 + -6x + (21x + 3x2)) Combine like terms: -6x + 21x = 15x 0 = 4 + (-42 + 15x + 3x2) Combine like terms: 4 + -42 = -38 0 = -38 + 15x + 3x2 Solving 0 = -38 + 15x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 38 = 38 38 + -15x + -3x2 = -38 + 15x + 3x2 + 38 + -15x + -3x2 Reorder the terms: 38 + -15x + -3x2 = -38 + 38 + 15x + -15x + 3x2 + -3x2 Combine like terms: -38 + 38 = 0 38 + -15x + -3x2 = 0 + 15x + -15x + 3x2 + -3x2 38 + -15x + -3x2 = 15x + -15x + 3x2 + -3x2 Combine like terms: 15x + -15x = 0 38 + -15x + -3x2 = 0 + 3x2 + -3x2 38 + -15x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 38 + -15x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -12.66666667 + 5x + x2 = 0 Move the constant term to the right: Add '12.66666667' to each side of the equation. -12.66666667 + 5x + 12.66666667 + x2 = 0 + 12.66666667 Reorder the terms: -12.66666667 + 12.66666667 + 5x + x2 = 0 + 12.66666667 Combine like terms: -12.66666667 + 12.66666667 = 0.00000000 0.00000000 + 5x + x2 = 0 + 12.66666667 5x + x2 = 0 + 12.66666667 Combine like terms: 0 + 12.66666667 = 12.66666667 5x + x2 = 12.66666667 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 = 12.66666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 12.66666667 + 6.25 Combine like terms: 12.66666667 + 6.25 = 18.91666667 6.25 + 5x + x2 = 18.91666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 18.91666667 Calculate the square root of the right side: 4.349329451 Break this problem into two subproblems by setting (x + 2.5) equal to 4.349329451 and -4.349329451.Subproblem 1
x + 2.5 = 4.349329451 Simplifying x + 2.5 = 4.349329451 Reorder the terms: 2.5 + x = 4.349329451 Solving 2.5 + x = 4.349329451 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 = 4.349329451 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.349329451 + -2.5 x = 4.349329451 + -2.5 Combine like terms: 4.349329451 + -2.5 = 1.849329451 x = 1.849329451 Simplifying x = 1.849329451Subproblem 2
x + 2.5 = -4.349329451 Simplifying x + 2.5 = -4.349329451 Reorder the terms: 2.5 + x = -4.349329451 Solving 2.5 + x = -4.349329451 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 = -4.349329451 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.349329451 + -2.5 x = -4.349329451 + -2.5 Combine like terms: -4.349329451 + -2.5 = -6.849329451 x = -6.849329451 Simplifying x = -6.849329451Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.849329451, -6.849329451}
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