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Simplifying x(5x + -2) + 2x(x + -1) = 45 Reorder the terms: x(-2 + 5x) + 2x(x + -1) = 45 (-2 * x + 5x * x) + 2x(x + -1) = 45 (-2x + 5x2) + 2x(x + -1) = 45 Reorder the terms: -2x + 5x2 + 2x(-1 + x) = 45 -2x + 5x2 + (-1 * 2x + x * 2x) = 45 -2x + 5x2 + (-2x + 2x2) = 45 Reorder the terms: -2x + -2x + 5x2 + 2x2 = 45 Combine like terms: -2x + -2x = -4x -4x + 5x2 + 2x2 = 45 Combine like terms: 5x2 + 2x2 = 7x2 -4x + 7x2 = 45 Solving -4x + 7x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -4x + 7x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.428571429 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '6.428571429' to each side of the equation. -6.428571429 + -0.5714285714x + 6.428571429 + x2 = 0 + 6.428571429 Reorder the terms: -6.428571429 + 6.428571429 + -0.5714285714x + x2 = 0 + 6.428571429 Combine like terms: -6.428571429 + 6.428571429 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 6.428571429 -0.5714285714x + x2 = 0 + 6.428571429 Combine like terms: 0 + 6.428571429 = 6.428571429 -0.5714285714x + x2 = 6.428571429 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 6.428571429 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 6.428571429 + 0.08163265305 Combine like terms: 6.428571429 + 0.08163265305 = 6.51020408205 0.08163265305 + -0.5714285714x + x2 = 6.51020408205 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 6.51020408205 Calculate the square root of the right side: 2.551510157 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 2.551510157 and -2.551510157.Subproblem 1
x + -0.2857142857 = 2.551510157 Simplifying x + -0.2857142857 = 2.551510157 Reorder the terms: -0.2857142857 + x = 2.551510157 Solving -0.2857142857 + x = 2.551510157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 2.551510157 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 2.551510157 + 0.2857142857 x = 2.551510157 + 0.2857142857 Combine like terms: 2.551510157 + 0.2857142857 = 2.8372244427 x = 2.8372244427 Simplifying x = 2.8372244427Subproblem 2
x + -0.2857142857 = -2.551510157 Simplifying x + -0.2857142857 = -2.551510157 Reorder the terms: -0.2857142857 + x = -2.551510157 Solving -0.2857142857 + x = -2.551510157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -2.551510157 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -2.551510157 + 0.2857142857 x = -2.551510157 + 0.2857142857 Combine like terms: -2.551510157 + 0.2857142857 = -2.2657958713 x = -2.2657958713 Simplifying x = -2.2657958713Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8372244427, -2.2657958713}
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