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Simplifying 5x(3x + 2) = -5 + -2(7x + -6) Reorder the terms: 5x(2 + 3x) = -5 + -2(7x + -6) (2 * 5x + 3x * 5x) = -5 + -2(7x + -6) (10x + 15x2) = -5 + -2(7x + -6) Reorder the terms: 10x + 15x2 = -5 + -2(-6 + 7x) 10x + 15x2 = -5 + (-6 * -2 + 7x * -2) 10x + 15x2 = -5 + (12 + -14x) Combine like terms: -5 + 12 = 7 10x + 15x2 = 7 + -14x Solving 10x + 15x2 = 7 + -14x Solving for variable 'x'. Reorder the terms: -7 + 10x + 14x + 15x2 = 7 + -14x + -7 + 14x Combine like terms: 10x + 14x = 24x -7 + 24x + 15x2 = 7 + -14x + -7 + 14x Reorder the terms: -7 + 24x + 15x2 = 7 + -7 + -14x + 14x Combine like terms: 7 + -7 = 0 -7 + 24x + 15x2 = 0 + -14x + 14x -7 + 24x + 15x2 = -14x + 14x Combine like terms: -14x + 14x = 0 -7 + 24x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4666666667 + 1.6x + x2 = 0 Move the constant term to the right: Add '0.4666666667' to each side of the equation. -0.4666666667 + 1.6x + 0.4666666667 + x2 = 0 + 0.4666666667 Reorder the terms: -0.4666666667 + 0.4666666667 + 1.6x + x2 = 0 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + 1.6x + x2 = 0 + 0.4666666667 1.6x + x2 = 0 + 0.4666666667 Combine like terms: 0 + 0.4666666667 = 0.4666666667 1.6x + x2 = 0.4666666667 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 = 0.4666666667 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 0.4666666667 + 0.64 Combine like terms: 0.4666666667 + 0.64 = 1.1066666667 0.64 + 1.6x + x2 = 1.1066666667 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 1.1066666667 Calculate the square root of the right side: 1.051982256 Break this problem into two subproblems by setting (x + 0.8) equal to 1.051982256 and -1.051982256.Subproblem 1
x + 0.8 = 1.051982256 Simplifying x + 0.8 = 1.051982256 Reorder the terms: 0.8 + x = 1.051982256 Solving 0.8 + x = 1.051982256 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 = 1.051982256 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.051982256 + -0.8 x = 1.051982256 + -0.8 Combine like terms: 1.051982256 + -0.8 = 0.251982256 x = 0.251982256 Simplifying x = 0.251982256Subproblem 2
x + 0.8 = -1.051982256 Simplifying x + 0.8 = -1.051982256 Reorder the terms: 0.8 + x = -1.051982256 Solving 0.8 + x = -1.051982256 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 = -1.051982256 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.051982256 + -0.8 x = -1.051982256 + -0.8 Combine like terms: -1.051982256 + -0.8 = -1.851982256 x = -1.851982256 Simplifying x = -1.851982256Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.251982256, -1.851982256}
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