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Simplifying (10x2 + 5x + 3) + (2x2 + -7x + 5) = 0 Reorder the terms: (3 + 5x + 10x2) + (2x2 + -7x + 5) = 0 Remove parenthesis around (3 + 5x + 10x2) 3 + 5x + 10x2 + (2x2 + -7x + 5) = 0 Reorder the terms: 3 + 5x + 10x2 + (5 + -7x + 2x2) = 0 Remove parenthesis around (5 + -7x + 2x2) 3 + 5x + 10x2 + 5 + -7x + 2x2 = 0 Reorder the terms: 3 + 5 + 5x + -7x + 10x2 + 2x2 = 0 Combine like terms: 3 + 5 = 8 8 + 5x + -7x + 10x2 + 2x2 = 0 Combine like terms: 5x + -7x = -2x 8 + -2x + 10x2 + 2x2 = 0 Combine like terms: 10x2 + 2x2 = 12x2 8 + -2x + 12x2 = 0 Solving 8 + -2x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -1x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1x + 6x2)' equal to zero and attempt to solve: Simplifying 4 + -1x + 6x2 = 0 Solving 4 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.1666666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.1666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.1666666667x + x2 = 0 + -0.6666666667 -0.1666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.1666666667x + x2 = -0.6666666667 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = -0.6666666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = -0.6666666667 + 0.006944444447 Combine like terms: -0.6666666667 + 0.006944444447 = -0.659722222253 0.006944444447 + -0.1666666667x + x2 = -0.659722222253 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = -0.659722222253 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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