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Simplifying (4x2 + 6x + -7) + -1(5x2 + -4x + 3) = 0 Reorder the terms: (-7 + 6x + 4x2) + -1(5x2 + -4x + 3) = 0 Remove parenthesis around (-7 + 6x + 4x2) -7 + 6x + 4x2 + -1(5x2 + -4x + 3) = 0 Reorder the terms: -7 + 6x + 4x2 + -1(3 + -4x + 5x2) = 0 -7 + 6x + 4x2 + (3 * -1 + -4x * -1 + 5x2 * -1) = 0 -7 + 6x + 4x2 + (-3 + 4x + -5x2) = 0 Reorder the terms: -7 + -3 + 6x + 4x + 4x2 + -5x2 = 0 Combine like terms: -7 + -3 = -10 -10 + 6x + 4x + 4x2 + -5x2 = 0 Combine like terms: 6x + 4x = 10x -10 + 10x + 4x2 + -5x2 = 0 Combine like terms: 4x2 + -5x2 = -1x2 -10 + 10x + -1x2 = 0 Solving -10 + 10x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -10x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -10x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10x + x2 = 0 + -10 -10x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -10x + x2 = -10 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -10 + 25 Reorder the terms: 25 + -10x + x2 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + -10x + x2 = 15 Factor a perfect square on the left side: (x + -5)(x + -5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -5) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -5 = 3.872983346 Simplifying x + -5 = 3.872983346 Reorder the terms: -5 + x = 3.872983346 Solving -5 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.872983346 + 5 x = 3.872983346 + 5 Combine like terms: 3.872983346 + 5 = 8.872983346 x = 8.872983346 Simplifying x = 8.872983346Subproblem 2
x + -5 = -3.872983346 Simplifying x + -5 = -3.872983346 Reorder the terms: -5 + x = -3.872983346 Solving -5 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.872983346 + 5 x = -3.872983346 + 5 Combine like terms: -3.872983346 + 5 = 1.127016654 x = 1.127016654 Simplifying x = 1.127016654Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.872983346, 1.127016654}
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