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Simplifying (-7x2 + -10x + -50) + -1(5x + 2 + 20) = 0 Reorder the terms: (-50 + -10x + -7x2) + -1(5x + 2 + 20) = 0 Remove parenthesis around (-50 + -10x + -7x2) -50 + -10x + -7x2 + -1(5x + 2 + 20) = 0 Reorder the terms: -50 + -10x + -7x2 + -1(2 + 20 + 5x) = 0 Combine like terms: 2 + 20 = 22 -50 + -10x + -7x2 + -1(22 + 5x) = 0 -50 + -10x + -7x2 + (22 * -1 + 5x * -1) = 0 -50 + -10x + -7x2 + (-22 + -5x) = 0 Reorder the terms: -50 + -22 + -10x + -5x + -7x2 = 0 Combine like terms: -50 + -22 = -72 -72 + -10x + -5x + -7x2 = 0 Combine like terms: -10x + -5x = -15x -72 + -15x + -7x2 = 0 Solving -72 + -15x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(72 + 15x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(72 + 15x + 7x2)' equal to zero and attempt to solve: Simplifying 72 + 15x + 7x2 = 0 Solving 72 + 15x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 10.28571429 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '-10.28571429' to each side of the equation. 10.28571429 + 2.142857143x + -10.28571429 + x2 = 0 + -10.28571429 Reorder the terms: 10.28571429 + -10.28571429 + 2.142857143x + x2 = 0 + -10.28571429 Combine like terms: 10.28571429 + -10.28571429 = 0.00000000 0.00000000 + 2.142857143x + x2 = 0 + -10.28571429 2.142857143x + x2 = 0 + -10.28571429 Combine like terms: 0 + -10.28571429 = -10.28571429 2.142857143x + x2 = -10.28571429 The x term is 2.142857143x. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143x + 1.147959185 + x2 = -10.28571429 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = -10.28571429 + 1.147959185 Combine like terms: -10.28571429 + 1.147959185 = -9.137755105 1.147959185 + 2.142857143x + x2 = -9.137755105 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = -9.137755105 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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