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Simplifying 5x(7x + -3x) = 16x + 15 Combine like terms: 7x + -3x = 4x 5x(4x) = 16x + 15 Remove parenthesis around (4x) 5x * 4x = 16x + 15 Reorder the terms for easier multiplication: 5 * 4x * x = 16x + 15 Multiply 5 * 4 20x * x = 16x + 15 Multiply x * x 20x2 = 16x + 15 Reorder the terms: 20x2 = 15 + 16x Solving 20x2 = 15 + 16x Solving for variable 'x'. Reorder the terms: -15 + -16x + 20x2 = 15 + 16x + -15 + -16x Reorder the terms: -15 + -16x + 20x2 = 15 + -15 + 16x + -16x Combine like terms: 15 + -15 = 0 -15 + -16x + 20x2 = 0 + 16x + -16x -15 + -16x + 20x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -15 + -16x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.75 + -0.8x + x2 = 0.0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.8x + 0.75 + x2 = 0.0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.8x + x2 = 0.0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.8x + x2 = 0.0 + 0.75 -0.8x + x2 = 0.0 + 0.75 Combine like terms: 0.0 + 0.75 = 0.75 -0.8x + x2 = 0.75 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.75 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.75 + 0.16 Combine like terms: 0.75 + 0.16 = 0.91 0.16 + -0.8x + x2 = 0.91 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.91 Calculate the square root of the right side: 0.953939201 Break this problem into two subproblems by setting (x + -0.4) equal to 0.953939201 and -0.953939201.Subproblem 1
x + -0.4 = 0.953939201 Simplifying x + -0.4 = 0.953939201 Reorder the terms: -0.4 + x = 0.953939201 Solving -0.4 + x = 0.953939201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.953939201 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.953939201 + 0.4 x = 0.953939201 + 0.4 Combine like terms: 0.953939201 + 0.4 = 1.353939201 x = 1.353939201 Simplifying x = 1.353939201Subproblem 2
x + -0.4 = -0.953939201 Simplifying x + -0.4 = -0.953939201 Reorder the terms: -0.4 + x = -0.953939201 Solving -0.4 + x = -0.953939201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.953939201 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.953939201 + 0.4 x = -0.953939201 + 0.4 Combine like terms: -0.953939201 + 0.4 = -0.553939201 x = -0.553939201 Simplifying x = -0.553939201Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.353939201, -0.553939201}
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