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Simplifying 5x(3 + 2x) = 18 + -1(x + -1) (3 * 5x + 2x * 5x) = 18 + -1(x + -1) (15x + 10x2) = 18 + -1(x + -1) Reorder the terms: 15x + 10x2 = 18 + -1(-1 + x) 15x + 10x2 = 18 + (-1 * -1 + x * -1) 15x + 10x2 = 18 + (1 + -1x) Combine like terms: 18 + 1 = 19 15x + 10x2 = 19 + -1x Solving 15x + 10x2 = 19 + -1x Solving for variable 'x'. Reorder the terms: -19 + 15x + x + 10x2 = 19 + -1x + -19 + x Combine like terms: 15x + x = 16x -19 + 16x + 10x2 = 19 + -1x + -19 + x Reorder the terms: -19 + 16x + 10x2 = 19 + -19 + -1x + x Combine like terms: 19 + -19 = 0 -19 + 16x + 10x2 = 0 + -1x + x -19 + 16x + 10x2 = -1x + x Combine like terms: -1x + x = 0 -19 + 16x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.9 + 1.6x + x2 = 0.0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + 1.6x + 1.9 + x2 = 0.0 + 1.9 Reorder the terms: -1.9 + 1.9 + 1.6x + x2 = 0.0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + 1.6x + x2 = 0.0 + 1.9 1.6x + x2 = 0.0 + 1.9 Combine like terms: 0.0 + 1.9 = 1.9 1.6x + x2 = 1.9 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 1.9 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 1.9 + 0.64 Combine like terms: 1.9 + 0.64 = 2.54 0.64 + 1.6x + x2 = 2.54 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 2.54 Calculate the square root of the right side: 1.593737745 Break this problem into two subproblems by setting (x + 0.8) equal to 1.593737745 and -1.593737745.Subproblem 1
x + 0.8 = 1.593737745 Simplifying x + 0.8 = 1.593737745 Reorder the terms: 0.8 + x = 1.593737745 Solving 0.8 + x = 1.593737745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.593737745 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.593737745 + -0.8 x = 1.593737745 + -0.8 Combine like terms: 1.593737745 + -0.8 = 0.793737745 x = 0.793737745 Simplifying x = 0.793737745Subproblem 2
x + 0.8 = -1.593737745 Simplifying x + 0.8 = -1.593737745 Reorder the terms: 0.8 + x = -1.593737745 Solving 0.8 + x = -1.593737745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.593737745 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.593737745 + -0.8 x = -1.593737745 + -0.8 Combine like terms: -1.593737745 + -0.8 = -2.393737745 x = -2.393737745 Simplifying x = -2.393737745Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.793737745, -2.393737745}
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