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Simplifying (6x * 6x) + -1((4x * 4x) + -3x + 5) = 0 Reorder the terms for easier multiplication: (6 * 6x * x) + -1((4x * 4x) + -3x + 5) = 0 Multiply 6 * 6 (36x * x) + -1((4x * 4x) + -3x + 5) = 0 Multiply x * x (36x2) + -1((4x * 4x) + -3x + 5) = 0 Reorder the terms for easier multiplication: (36x2) + -1((4 * 4x * x) + -3x + 5) = 0 Multiply 4 * 4 (36x2) + -1((16x * x) + -3x + 5) = 0 Multiply x * x (36x2) + -1((16x2) + -3x + 5) = 0 Reorder the terms: (36x2) + -1(5 + -3x + (16x2)) = 0 (36x2) + (5 * -1 + -3x * -1 + (16x2) * -1) = 0 (36x2) + (-5 + 3x + -16x2) = 0 Reorder the terms: -5 + 3x + (36x2) + -16x2 = 0 Combine like terms: (36x2) + -16x2 = 20x2 -5 + 3x + 20x2 = 0 Solving -5 + 3x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.25 + 0.15x + x2 = 0.0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.15x + 0.25 + x2 = 0.0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.15x + x2 = 0.0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.15x + x2 = 0.0 + 0.25 0.15x + x2 = 0.0 + 0.25 Combine like terms: 0.0 + 0.25 = 0.25 0.15x + x2 = 0.25 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = 0.25 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 0.25 + 0.005625 Combine like terms: 0.25 + 0.005625 = 0.255625 0.005625 + 0.15x + x2 = 0.255625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 0.255625 Calculate the square root of the right side: 0.50559371 Break this problem into two subproblems by setting (x + 0.075) equal to 0.50559371 and -0.50559371.Subproblem 1
x + 0.075 = 0.50559371 Simplifying x + 0.075 = 0.50559371 Reorder the terms: 0.075 + x = 0.50559371 Solving 0.075 + x = 0.50559371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 0.50559371 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.50559371 + -0.075 x = 0.50559371 + -0.075 Combine like terms: 0.50559371 + -0.075 = 0.43059371 x = 0.43059371 Simplifying x = 0.43059371Subproblem 2
x + 0.075 = -0.50559371 Simplifying x + 0.075 = -0.50559371 Reorder the terms: 0.075 + x = -0.50559371 Solving 0.075 + x = -0.50559371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -0.50559371 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.50559371 + -0.075 x = -0.50559371 + -0.075 Combine like terms: -0.50559371 + -0.075 = -0.58059371 x = -0.58059371 Simplifying x = -0.58059371Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.43059371, -0.58059371}
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