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Simplifying -7(x2 + 2) + -1(3x + 1) = 0 Reorder the terms: -7(2 + x2) + -1(3x + 1) = 0 (2 * -7 + x2 * -7) + -1(3x + 1) = 0 (-14 + -7x2) + -1(3x + 1) = 0 Reorder the terms: -14 + -7x2 + -1(1 + 3x) = 0 -14 + -7x2 + (1 * -1 + 3x * -1) = 0 -14 + -7x2 + (-1 + -3x) = 0 Reorder the terms: -14 + -1 + -3x + -7x2 = 0 Combine like terms: -14 + -1 = -15 -15 + -3x + -7x2 = 0 Solving -15 + -3x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 3x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 3x + 7x2)' equal to zero and attempt to solve: Simplifying 15 + 3x + 7x2 = 0 Solving 15 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.142857143 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '-2.142857143' to each side of the equation. 2.142857143 + 0.4285714286x + -2.142857143 + x2 = 0 + -2.142857143 Reorder the terms: 2.142857143 + -2.142857143 + 0.4285714286x + x2 = 0 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + -2.142857143 0.4285714286x + x2 = 0 + -2.142857143 Combine like terms: 0 + -2.142857143 = -2.142857143 0.4285714286x + x2 = -2.142857143 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = -2.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = -2.142857143 + 0.04591836735 Combine like terms: -2.142857143 + 0.04591836735 = -2.09693877565 0.04591836735 + 0.4285714286x + x2 = -2.09693877565 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = -2.09693877565 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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