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Simplifying (4x2 + -5x + -7) + -1(x2 + 9x + -3) = 0 Reorder the terms: (-7 + -5x + 4x2) + -1(x2 + 9x + -3) = 0 Remove parenthesis around (-7 + -5x + 4x2) -7 + -5x + 4x2 + -1(x2 + 9x + -3) = 0 Reorder the terms: -7 + -5x + 4x2 + -1(-3 + 9x + x2) = 0 -7 + -5x + 4x2 + (-3 * -1 + 9x * -1 + x2 * -1) = 0 -7 + -5x + 4x2 + (3 + -9x + -1x2) = 0 Reorder the terms: -7 + 3 + -5x + -9x + 4x2 + -1x2 = 0 Combine like terms: -7 + 3 = -4 -4 + -5x + -9x + 4x2 + -1x2 = 0 Combine like terms: -5x + -9x = -14x -4 + -14x + 4x2 + -1x2 = 0 Combine like terms: 4x2 + -1x2 = 3x2 -4 + -14x + 3x2 = 0 Solving -4 + -14x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -4.666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -4.666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -4.666666667x + x2 = 0 + 1.333333333 -4.666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -4.666666667x + x2 = 1.333333333 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 1.333333333 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 1.333333333 + 5.444444448 Combine like terms: 1.333333333 + 5.444444448 = 6.777777781 5.444444448 + -4.666666667x + x2 = 6.777777781 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 6.777777781 Calculate the square root of the right side: 2.603416559 Break this problem into two subproblems by setting (x + -2.333333334) equal to 2.603416559 and -2.603416559.Subproblem 1
x + -2.333333334 = 2.603416559 Simplifying x + -2.333333334 = 2.603416559 Reorder the terms: -2.333333334 + x = 2.603416559 Solving -2.333333334 + x = 2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.603416559 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.603416559 + 2.333333334 x = 2.603416559 + 2.333333334 Combine like terms: 2.603416559 + 2.333333334 = 4.936749893 x = 4.936749893 Simplifying x = 4.936749893Subproblem 2
x + -2.333333334 = -2.603416559 Simplifying x + -2.333333334 = -2.603416559 Reorder the terms: -2.333333334 + x = -2.603416559 Solving -2.333333334 + x = -2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.603416559 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.603416559 + 2.333333334 x = -2.603416559 + 2.333333334 Combine like terms: -2.603416559 + 2.333333334 = -0.270083225 x = -0.270083225 Simplifying x = -0.270083225Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.936749893, -0.270083225}
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