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Simplifying 5x2 + 4x2 + -35x + -28 = 0 Reorder the terms: -28 + -35x + 5x2 + 4x2 = 0 Combine like terms: 5x2 + 4x2 = 9x2 -28 + -35x + 9x2 = 0 Solving -28 + -35x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + -3.888888889x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + -3.888888889x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + -3.888888889x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + -3.888888889x + x2 = 0 + 3.111111111 -3.888888889x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 -3.888888889x + x2 = 3.111111111 The x term is -3.888888889x. Take half its coefficient (-1.944444445). Square it (3.780864200) and add it to both sides. Add '3.780864200' to each side of the equation. -3.888888889x + 3.780864200 + x2 = 3.111111111 + 3.780864200 Reorder the terms: 3.780864200 + -3.888888889x + x2 = 3.111111111 + 3.780864200 Combine like terms: 3.111111111 + 3.780864200 = 6.891975311 3.780864200 + -3.888888889x + x2 = 6.891975311 Factor a perfect square on the left side: (x + -1.944444445)(x + -1.944444445) = 6.891975311 Calculate the square root of the right side: 2.625257189 Break this problem into two subproblems by setting (x + -1.944444445) equal to 2.625257189 and -2.625257189.Subproblem 1
x + -1.944444445 = 2.625257189 Simplifying x + -1.944444445 = 2.625257189 Reorder the terms: -1.944444445 + x = 2.625257189 Solving -1.944444445 + x = 2.625257189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x = 2.625257189 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x = 2.625257189 + 1.944444445 x = 2.625257189 + 1.944444445 Combine like terms: 2.625257189 + 1.944444445 = 4.569701634 x = 4.569701634 Simplifying x = 4.569701634Subproblem 2
x + -1.944444445 = -2.625257189 Simplifying x + -1.944444445 = -2.625257189 Reorder the terms: -1.944444445 + x = -2.625257189 Solving -1.944444445 + x = -2.625257189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x = -2.625257189 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x = -2.625257189 + 1.944444445 x = -2.625257189 + 1.944444445 Combine like terms: -2.625257189 + 1.944444445 = -0.680812744 x = -0.680812744 Simplifying x = -0.680812744Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.569701634, -0.680812744}
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