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Simplifying 7r * 7r = 70r + -175 Reorder the terms for easier multiplication: 7 * 7r * r = 70r + -175 Multiply 7 * 7 49r * r = 70r + -175 Multiply r * r 49r2 = 70r + -175 Reorder the terms: 49r2 = -175 + 70r Solving 49r2 = -175 + 70r Solving for variable 'r'. Reorder the terms: 175 + -70r + 49r2 = -175 + 70r + 175 + -70r Reorder the terms: 175 + -70r + 49r2 = -175 + 175 + 70r + -70r Combine like terms: -175 + 175 = 0 175 + -70r + 49r2 = 0 + 70r + -70r 175 + -70r + 49r2 = 70r + -70r Combine like terms: 70r + -70r = 0 175 + -70r + 49r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(25 + -10r + 7r2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(25 + -10r + 7r2)' equal to zero and attempt to solve: Simplifying 25 + -10r + 7r2 = 0 Solving 25 + -10r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.571428571 + -1.428571429r + r2 = 0 Move the constant term to the right: Add '-3.571428571' to each side of the equation. 3.571428571 + -1.428571429r + -3.571428571 + r2 = 0 + -3.571428571 Reorder the terms: 3.571428571 + -3.571428571 + -1.428571429r + r2 = 0 + -3.571428571 Combine like terms: 3.571428571 + -3.571428571 = 0.000000000 0.000000000 + -1.428571429r + r2 = 0 + -3.571428571 -1.428571429r + r2 = 0 + -3.571428571 Combine like terms: 0 + -3.571428571 = -3.571428571 -1.428571429r + r2 = -3.571428571 The r term is -1.428571429r. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429r + 0.5102040819 + r2 = -3.571428571 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429r + r2 = -3.571428571 + 0.5102040819 Combine like terms: -3.571428571 + 0.5102040819 = -3.0612244891 0.5102040819 + -1.428571429r + r2 = -3.0612244891 Factor a perfect square on the left side: (r + -0.7142857145)(r + -0.7142857145) = -3.0612244891 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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