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Simplifying (2x2 + -4 + 7x + -6) + -1(-3x2 + 5 + -4x) = 0 Reorder the terms: (-4 + -6 + 7x + 2x2) + -1(-3x2 + 5 + -4x) = 0 Combine like terms: -4 + -6 = -10 (-10 + 7x + 2x2) + -1(-3x2 + 5 + -4x) = 0 Remove parenthesis around (-10 + 7x + 2x2) -10 + 7x + 2x2 + -1(-3x2 + 5 + -4x) = 0 Reorder the terms: -10 + 7x + 2x2 + -1(5 + -4x + -3x2) = 0 -10 + 7x + 2x2 + (5 * -1 + -4x * -1 + -3x2 * -1) = 0 -10 + 7x + 2x2 + (-5 + 4x + 3x2) = 0 Reorder the terms: -10 + -5 + 7x + 4x + 2x2 + 3x2 = 0 Combine like terms: -10 + -5 = -15 -15 + 7x + 4x + 2x2 + 3x2 = 0 Combine like terms: 7x + 4x = 11x -15 + 11x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -15 + 11x + 5x2 = 0 Solving -15 + 11x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + 2.2x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.2x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.2x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.2x + x2 = 0 + 3 2.2x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.2x + x2 = 3 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 3 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 3 + 1.21 Combine like terms: 3 + 1.21 = 4.21 1.21 + 2.2x + x2 = 4.21 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 4.21 Calculate the square root of the right side: 2.051828453 Break this problem into two subproblems by setting (x + 1.1) equal to 2.051828453 and -2.051828453.Subproblem 1
x + 1.1 = 2.051828453 Simplifying x + 1.1 = 2.051828453 Reorder the terms: 1.1 + x = 2.051828453 Solving 1.1 + x = 2.051828453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 2.051828453 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 2.051828453 + -1.1 x = 2.051828453 + -1.1 Combine like terms: 2.051828453 + -1.1 = 0.951828453 x = 0.951828453 Simplifying x = 0.951828453Subproblem 2
x + 1.1 = -2.051828453 Simplifying x + 1.1 = -2.051828453 Reorder the terms: 1.1 + x = -2.051828453 Solving 1.1 + x = -2.051828453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -2.051828453 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -2.051828453 + -1.1 x = -2.051828453 + -1.1 Combine like terms: -2.051828453 + -1.1 = -3.151828453 x = -3.151828453 Simplifying x = -3.151828453Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.951828453, -3.151828453}
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