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Simplifying 3x(2x) + -5x(7 + -2x) = 10 + -4x + 5 Remove parenthesis around (2x) 3x * 2x + -5x(7 + -2x) = 10 + -4x + 5 Reorder the terms for easier multiplication: 3 * 2x * x + -5x(7 + -2x) = 10 + -4x + 5 Multiply 3 * 2 6x * x + -5x(7 + -2x) = 10 + -4x + 5 Multiply x * x 6x2 + -5x(7 + -2x) = 10 + -4x + 5 6x2 + (7 * -5x + -2x * -5x) = 10 + -4x + 5 6x2 + (-35x + 10x2) = 10 + -4x + 5 Reorder the terms: -35x + 6x2 + 10x2 = 10 + -4x + 5 Combine like terms: 6x2 + 10x2 = 16x2 -35x + 16x2 = 10 + -4x + 5 Reorder the terms: -35x + 16x2 = 10 + 5 + -4x Combine like terms: 10 + 5 = 15 -35x + 16x2 = 15 + -4x Solving -35x + 16x2 = 15 + -4x Solving for variable 'x'. Reorder the terms: -15 + -35x + 4x + 16x2 = 15 + -4x + -15 + 4x Combine like terms: -35x + 4x = -31x -15 + -31x + 16x2 = 15 + -4x + -15 + 4x Reorder the terms: -15 + -31x + 16x2 = 15 + -15 + -4x + 4x Combine like terms: 15 + -15 = 0 -15 + -31x + 16x2 = 0 + -4x + 4x -15 + -31x + 16x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -15 + -31x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -1.9375x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -1.9375x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -1.9375x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -1.9375x + x2 = 0 + 0.9375 -1.9375x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -1.9375x + x2 = 0.9375 The x term is -1.9375x. Take half its coefficient (-0.96875). Square it (0.9384765625) and add it to both sides. Add '0.9384765625' to each side of the equation. -1.9375x + 0.9384765625 + x2 = 0.9375 + 0.9384765625 Reorder the terms: 0.9384765625 + -1.9375x + x2 = 0.9375 + 0.9384765625 Combine like terms: 0.9375 + 0.9384765625 = 1.8759765625 0.9384765625 + -1.9375x + x2 = 1.8759765625 Factor a perfect square on the left side: (x + -0.96875)(x + -0.96875) = 1.8759765625 Calculate the square root of the right side: 1.369662938 Break this problem into two subproblems by setting (x + -0.96875) equal to 1.369662938 and -1.369662938.Subproblem 1
x + -0.96875 = 1.369662938 Simplifying x + -0.96875 = 1.369662938 Reorder the terms: -0.96875 + x = 1.369662938 Solving -0.96875 + x = 1.369662938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + x = 1.369662938 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = 1.369662938 + 0.96875 x = 1.369662938 + 0.96875 Combine like terms: 1.369662938 + 0.96875 = 2.338412938 x = 2.338412938 Simplifying x = 2.338412938Subproblem 2
x + -0.96875 = -1.369662938 Simplifying x + -0.96875 = -1.369662938 Reorder the terms: -0.96875 + x = -1.369662938 Solving -0.96875 + x = -1.369662938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + x = -1.369662938 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = -1.369662938 + 0.96875 x = -1.369662938 + 0.96875 Combine like terms: -1.369662938 + 0.96875 = -0.400912938 x = -0.400912938 Simplifying x = -0.400912938Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.338412938, -0.400912938}
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