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Simplifying 7a * 5a = 6a + 24 Reorder the terms for easier multiplication: 7 * 5a * a = 6a + 24 Multiply 7 * 5 35a * a = 6a + 24 Multiply a * a 35a2 = 6a + 24 Reorder the terms: 35a2 = 24 + 6a Solving 35a2 = 24 + 6a Solving for variable 'a'. Reorder the terms: -24 + -6a + 35a2 = 24 + 6a + -24 + -6a Reorder the terms: -24 + -6a + 35a2 = 24 + -24 + 6a + -6a Combine like terms: 24 + -24 = 0 -24 + -6a + 35a2 = 0 + 6a + -6a -24 + -6a + 35a2 = 6a + -6a Combine like terms: 6a + -6a = 0 -24 + -6a + 35a2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.6857142857 + -0.1714285714a + a2 = 0 Move the constant term to the right: Add '0.6857142857' to each side of the equation. -0.6857142857 + -0.1714285714a + 0.6857142857 + a2 = 0 + 0.6857142857 Reorder the terms: -0.6857142857 + 0.6857142857 + -0.1714285714a + a2 = 0 + 0.6857142857 Combine like terms: -0.6857142857 + 0.6857142857 = 0.0000000000 0.0000000000 + -0.1714285714a + a2 = 0 + 0.6857142857 -0.1714285714a + a2 = 0 + 0.6857142857 Combine like terms: 0 + 0.6857142857 = 0.6857142857 -0.1714285714a + a2 = 0.6857142857 The a term is -0.1714285714a. Take half its coefficient (-0.0857142857). Square it (0.007346938773) and add it to both sides. Add '0.007346938773' to each side of the equation. -0.1714285714a + 0.007346938773 + a2 = 0.6857142857 + 0.007346938773 Reorder the terms: 0.007346938773 + -0.1714285714a + a2 = 0.6857142857 + 0.007346938773 Combine like terms: 0.6857142857 + 0.007346938773 = 0.693061224473 0.007346938773 + -0.1714285714a + a2 = 0.693061224473 Factor a perfect square on the left side: (a + -0.0857142857)(a + -0.0857142857) = 0.693061224473 Calculate the square root of the right side: 0.832502988 Break this problem into two subproblems by setting (a + -0.0857142857) equal to 0.832502988 and -0.832502988.Subproblem 1
a + -0.0857142857 = 0.832502988 Simplifying a + -0.0857142857 = 0.832502988 Reorder the terms: -0.0857142857 + a = 0.832502988 Solving -0.0857142857 + a = 0.832502988 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.0857142857' to each side of the equation. -0.0857142857 + 0.0857142857 + a = 0.832502988 + 0.0857142857 Combine like terms: -0.0857142857 + 0.0857142857 = 0.0000000000 0.0000000000 + a = 0.832502988 + 0.0857142857 a = 0.832502988 + 0.0857142857 Combine like terms: 0.832502988 + 0.0857142857 = 0.9182172737 a = 0.9182172737 Simplifying a = 0.9182172737Subproblem 2
a + -0.0857142857 = -0.832502988 Simplifying a + -0.0857142857 = -0.832502988 Reorder the terms: -0.0857142857 + a = -0.832502988 Solving -0.0857142857 + a = -0.832502988 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.0857142857' to each side of the equation. -0.0857142857 + 0.0857142857 + a = -0.832502988 + 0.0857142857 Combine like terms: -0.0857142857 + 0.0857142857 = 0.0000000000 0.0000000000 + a = -0.832502988 + 0.0857142857 a = -0.832502988 + 0.0857142857 Combine like terms: -0.832502988 + 0.0857142857 = -0.7467887023 a = -0.7467887023 Simplifying a = -0.7467887023Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.9182172737, -0.7467887023}
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