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Simplifying (4x2 + -6x + 7) + (-19x2 + -15x + -18) = 0 Reorder the terms: (7 + -6x + 4x2) + (-19x2 + -15x + -18) = 0 Remove parenthesis around (7 + -6x + 4x2) 7 + -6x + 4x2 + (-19x2 + -15x + -18) = 0 Reorder the terms: 7 + -6x + 4x2 + (-18 + -15x + -19x2) = 0 Remove parenthesis around (-18 + -15x + -19x2) 7 + -6x + 4x2 + -18 + -15x + -19x2 = 0 Reorder the terms: 7 + -18 + -6x + -15x + 4x2 + -19x2 = 0 Combine like terms: 7 + -18 = -11 -11 + -6x + -15x + 4x2 + -19x2 = 0 Combine like terms: -6x + -15x = -21x -11 + -21x + 4x2 + -19x2 = 0 Combine like terms: 4x2 + -19x2 = -15x2 -11 + -21x + -15x2 = 0 Solving -11 + -21x + -15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 21x + 15x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 21x + 15x2)' equal to zero and attempt to solve: Simplifying 11 + 21x + 15x2 = 0 Solving 11 + 21x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.7333333333 + 1.4x + x2 = 0 Move the constant term to the right: Add '-0.7333333333' to each side of the equation. 0.7333333333 + 1.4x + -0.7333333333 + x2 = 0 + -0.7333333333 Reorder the terms: 0.7333333333 + -0.7333333333 + 1.4x + x2 = 0 + -0.7333333333 Combine like terms: 0.7333333333 + -0.7333333333 = 0.0000000000 0.0000000000 + 1.4x + x2 = 0 + -0.7333333333 1.4x + x2 = 0 + -0.7333333333 Combine like terms: 0 + -0.7333333333 = -0.7333333333 1.4x + x2 = -0.7333333333 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -0.7333333333 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -0.7333333333 + 0.49 Combine like terms: -0.7333333333 + 0.49 = -0.2433333333 0.49 + 1.4x + x2 = -0.2433333333 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -0.2433333333 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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