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Simplifying (3x2 + -4x + 17) + (7x2 + 7x + -75) = 0 Reorder the terms: (17 + -4x + 3x2) + (7x2 + 7x + -75) = 0 Remove parenthesis around (17 + -4x + 3x2) 17 + -4x + 3x2 + (7x2 + 7x + -75) = 0 Reorder the terms: 17 + -4x + 3x2 + (-75 + 7x + 7x2) = 0 Remove parenthesis around (-75 + 7x + 7x2) 17 + -4x + 3x2 + -75 + 7x + 7x2 = 0 Reorder the terms: 17 + -75 + -4x + 7x + 3x2 + 7x2 = 0 Combine like terms: 17 + -75 = -58 -58 + -4x + 7x + 3x2 + 7x2 = 0 Combine like terms: -4x + 7x = 3x -58 + 3x + 3x2 + 7x2 = 0 Combine like terms: 3x2 + 7x2 = 10x2 -58 + 3x + 10x2 = 0 Solving -58 + 3x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -5.8 + 0.3x + x2 = 0.0 Move the constant term to the right: Add '5.8' to each side of the equation. -5.8 + 0.3x + 5.8 + x2 = 0.0 + 5.8 Reorder the terms: -5.8 + 5.8 + 0.3x + x2 = 0.0 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + 0.3x + x2 = 0.0 + 5.8 0.3x + x2 = 0.0 + 5.8 Combine like terms: 0.0 + 5.8 = 5.8 0.3x + x2 = 5.8 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 5.8 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 5.8 + 0.0225 Combine like terms: 5.8 + 0.0225 = 5.8225 0.0225 + 0.3x + x2 = 5.8225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 5.8225 Calculate the square root of the right side: 2.412985702 Break this problem into two subproblems by setting (x + 0.15) equal to 2.412985702 and -2.412985702.Subproblem 1
x + 0.15 = 2.412985702 Simplifying x + 0.15 = 2.412985702 Reorder the terms: 0.15 + x = 2.412985702 Solving 0.15 + x = 2.412985702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 2.412985702 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 2.412985702 + -0.15 x = 2.412985702 + -0.15 Combine like terms: 2.412985702 + -0.15 = 2.262985702 x = 2.262985702 Simplifying x = 2.262985702Subproblem 2
x + 0.15 = -2.412985702 Simplifying x + 0.15 = -2.412985702 Reorder the terms: 0.15 + x = -2.412985702 Solving 0.15 + x = -2.412985702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -2.412985702 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -2.412985702 + -0.15 x = -2.412985702 + -0.15 Combine like terms: -2.412985702 + -0.15 = -2.562985702 x = -2.562985702 Simplifying x = -2.562985702Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.262985702, -2.562985702}
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