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Simplifying x2 + -16x2 + -3x + -4 = 0 Reorder the terms: -4 + -3x + x2 + -16x2 = 0 Combine like terms: x2 + -16x2 = -15x2 -4 + -3x + -15x2 = 0 Solving -4 + -3x + -15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 3x + 15x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 3x + 15x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + 15x2 = 0 Solving 4 + 3x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.2666666667 + 0.2x + x2 = 0 Move the constant term to the right: Add '-0.2666666667' to each side of the equation. 0.2666666667 + 0.2x + -0.2666666667 + x2 = 0 + -0.2666666667 Reorder the terms: 0.2666666667 + -0.2666666667 + 0.2x + x2 = 0 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + 0.2x + x2 = 0 + -0.2666666667 0.2x + x2 = 0 + -0.2666666667 Combine like terms: 0 + -0.2666666667 = -0.2666666667 0.2x + x2 = -0.2666666667 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = -0.2666666667 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = -0.2666666667 + 0.01 Combine like terms: -0.2666666667 + 0.01 = -0.2566666667 0.01 + 0.2x + x2 = -0.2566666667 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = -0.2566666667 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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