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Simplifying 10x2 + 7x + -11 = 5x2 + 4 Reorder the terms: -11 + 7x + 10x2 = 5x2 + 4 Reorder the terms: -11 + 7x + 10x2 = 4 + 5x2 Solving -11 + 7x + 10x2 = 4 + 5x2 Solving for variable 'x'. Reorder the terms: -11 + -4 + 7x + 10x2 + -5x2 = 4 + 5x2 + -4 + -5x2 Combine like terms: -11 + -4 = -15 -15 + 7x + 10x2 + -5x2 = 4 + 5x2 + -4 + -5x2 Combine like terms: 10x2 + -5x2 = 5x2 -15 + 7x + 5x2 = 4 + 5x2 + -4 + -5x2 Reorder the terms: -15 + 7x + 5x2 = 4 + -4 + 5x2 + -5x2 Combine like terms: 4 + -4 = 0 -15 + 7x + 5x2 = 0 + 5x2 + -5x2 -15 + 7x + 5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -15 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + 1.4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.4x + x2 = 0 + 3 1.4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.4x + x2 = 3 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 3 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 3 + 0.49 Combine like terms: 3 + 0.49 = 3.49 0.49 + 1.4x + x2 = 3.49 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (x + 0.7) equal to 1.868154169 and -1.868154169.Subproblem 1
x + 0.7 = 1.868154169 Simplifying x + 0.7 = 1.868154169 Reorder the terms: 0.7 + x = 1.868154169 Solving 0.7 + x = 1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 1.868154169 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 1.868154169 + -0.7 x = 1.868154169 + -0.7 Combine like terms: 1.868154169 + -0.7 = 1.168154169 x = 1.168154169 Simplifying x = 1.168154169Subproblem 2
x + 0.7 = -1.868154169 Simplifying x + 0.7 = -1.868154169 Reorder the terms: 0.7 + x = -1.868154169 Solving 0.7 + x = -1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -1.868154169 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -1.868154169 + -0.7 x = -1.868154169 + -0.7 Combine like terms: -1.868154169 + -0.7 = -2.568154169 x = -2.568154169 Simplifying x = -2.568154169Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.168154169, -2.568154169}
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