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Simplifying (x + 10) * 3x + -4 = 15 Reorder the terms: (10 + x) * 3x + -4 = 15 Reorder the terms for easier multiplication: 3x(10 + x) + -4 = 15 (10 * 3x + x * 3x) + -4 = 15 (30x + 3x2) + -4 = 15 Reorder the terms: -4 + 30x + 3x2 = 15 Solving -4 + 30x + 3x2 = 15 Solving for variable 'x'. Reorder the terms: -4 + -15 + 30x + 3x2 = 15 + -15 Combine like terms: -4 + -15 = -19 -19 + 30x + 3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -19 + 30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.333333333 + 10x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + 10x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + 10x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + 10x + x2 = 0 + 6.333333333 10x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 10x + x2 = 6.333333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 6.333333333 + 25 Reorder the terms: 25 + 10x + x2 = 6.333333333 + 25 Combine like terms: 6.333333333 + 25 = 31.333333333 25 + 10x + x2 = 31.333333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 31.333333333 Calculate the square root of the right side: 5.597618541 Break this problem into two subproblems by setting (x + 5) equal to 5.597618541 and -5.597618541.Subproblem 1
x + 5 = 5.597618541 Simplifying x + 5 = 5.597618541 Reorder the terms: 5 + x = 5.597618541 Solving 5 + x = 5.597618541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.597618541 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.597618541 + -5 x = 5.597618541 + -5 Combine like terms: 5.597618541 + -5 = 0.597618541 x = 0.597618541 Simplifying x = 0.597618541Subproblem 2
x + 5 = -5.597618541 Simplifying x + 5 = -5.597618541 Reorder the terms: 5 + x = -5.597618541 Solving 5 + x = -5.597618541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.597618541 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.597618541 + -5 x = -5.597618541 + -5 Combine like terms: -5.597618541 + -5 = -10.597618541 x = -10.597618541 Simplifying x = -10.597618541Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.597618541, -10.597618541}
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