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Simplifying (3 + -13x + -7x2) + -1(5x2 + 12x + -10) = 0 Remove parenthesis around (3 + -13x + -7x2) 3 + -13x + -7x2 + -1(5x2 + 12x + -10) = 0 Reorder the terms: 3 + -13x + -7x2 + -1(-10 + 12x + 5x2) = 0 3 + -13x + -7x2 + (-10 * -1 + 12x * -1 + 5x2 * -1) = 0 3 + -13x + -7x2 + (10 + -12x + -5x2) = 0 Reorder the terms: 3 + 10 + -13x + -12x + -7x2 + -5x2 = 0 Combine like terms: 3 + 10 = 13 13 + -13x + -12x + -7x2 + -5x2 = 0 Combine like terms: -13x + -12x = -25x 13 + -25x + -7x2 + -5x2 = 0 Combine like terms: -7x2 + -5x2 = -12x2 13 + -25x + -12x2 = 0 Solving 13 + -25x + -12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.083333333 + 2.083333333x + x2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + 2.083333333x + 1.083333333 + x2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + 2.083333333x + x2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + 2.083333333x + x2 = 0 + 1.083333333 2.083333333x + x2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 2.083333333x + x2 = 1.083333333 The x term is 2.083333333x. Take half its coefficient (1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. 2.083333333x + 1.085069445 + x2 = 1.083333333 + 1.085069445 Reorder the terms: 1.085069445 + 2.083333333x + x2 = 1.083333333 + 1.085069445 Combine like terms: 1.083333333 + 1.085069445 = 2.168402778 1.085069445 + 2.083333333x + x2 = 2.168402778 Factor a perfect square on the left side: (x + 1.041666667)(x + 1.041666667) = 2.168402778 Calculate the square root of the right side: 1.472549754 Break this problem into two subproblems by setting (x + 1.041666667) equal to 1.472549754 and -1.472549754.Subproblem 1
x + 1.041666667 = 1.472549754 Simplifying x + 1.041666667 = 1.472549754 Reorder the terms: 1.041666667 + x = 1.472549754 Solving 1.041666667 + x = 1.472549754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + x = 1.472549754 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + x = 1.472549754 + -1.041666667 x = 1.472549754 + -1.041666667 Combine like terms: 1.472549754 + -1.041666667 = 0.430883087 x = 0.430883087 Simplifying x = 0.430883087Subproblem 2
x + 1.041666667 = -1.472549754 Simplifying x + 1.041666667 = -1.472549754 Reorder the terms: 1.041666667 + x = -1.472549754 Solving 1.041666667 + x = -1.472549754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + x = -1.472549754 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + x = -1.472549754 + -1.041666667 x = -1.472549754 + -1.041666667 Combine like terms: -1.472549754 + -1.041666667 = -2.514216421 x = -2.514216421 Simplifying x = -2.514216421Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.430883087, -2.514216421}
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