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Simplifying (7x2 + -2x + 28) + (3x2 + 9x + -71) = 0 Reorder the terms: (28 + -2x + 7x2) + (3x2 + 9x + -71) = 0 Remove parenthesis around (28 + -2x + 7x2) 28 + -2x + 7x2 + (3x2 + 9x + -71) = 0 Reorder the terms: 28 + -2x + 7x2 + (-71 + 9x + 3x2) = 0 Remove parenthesis around (-71 + 9x + 3x2) 28 + -2x + 7x2 + -71 + 9x + 3x2 = 0 Reorder the terms: 28 + -71 + -2x + 9x + 7x2 + 3x2 = 0 Combine like terms: 28 + -71 = -43 -43 + -2x + 9x + 7x2 + 3x2 = 0 Combine like terms: -2x + 9x = 7x -43 + 7x + 7x2 + 3x2 = 0 Combine like terms: 7x2 + 3x2 = 10x2 -43 + 7x + 10x2 = 0 Solving -43 + 7x + 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'. -4.3 + 0.7x + x2 = 0.0 Move the constant term to the right: Add '4.3' to each side of the equation. -4.3 + 0.7x + 4.3 + x2 = 0.0 + 4.3 Reorder the terms: -4.3 + 4.3 + 0.7x + x2 = 0.0 + 4.3 Combine like terms: -4.3 + 4.3 = 0.0 0.0 + 0.7x + x2 = 0.0 + 4.3 0.7x + x2 = 0.0 + 4.3 Combine like terms: 0.0 + 4.3 = 4.3 0.7x + x2 = 4.3 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 4.3 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 4.3 + 0.1225 Combine like terms: 4.3 + 0.1225 = 4.4225 0.1225 + 0.7x + x2 = 4.4225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 4.4225 Calculate the square root of the right side: 2.102974084 Break this problem into two subproblems by setting (x + 0.35) equal to 2.102974084 and -2.102974084.Subproblem 1
x + 0.35 = 2.102974084 Simplifying x + 0.35 = 2.102974084 Reorder the terms: 0.35 + x = 2.102974084 Solving 0.35 + x = 2.102974084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 2.102974084 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 2.102974084 + -0.35 x = 2.102974084 + -0.35 Combine like terms: 2.102974084 + -0.35 = 1.752974084 x = 1.752974084 Simplifying x = 1.752974084Subproblem 2
x + 0.35 = -2.102974084 Simplifying x + 0.35 = -2.102974084 Reorder the terms: 0.35 + x = -2.102974084 Solving 0.35 + x = -2.102974084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -2.102974084 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -2.102974084 + -0.35 x = -2.102974084 + -0.35 Combine like terms: -2.102974084 + -0.35 = -2.452974084 x = -2.452974084 Simplifying x = -2.452974084Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.752974084, -2.452974084}
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