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Simplifying -16x2 + 46x + 6 = 30 Reorder the terms: 6 + 46x + -16x2 = 30 Solving 6 + 46x + -16x2 = 30 Solving for variable 'x'. Reorder the terms: 6 + -30 + 46x + -16x2 = 30 + -30 Combine like terms: 6 + -30 = -24 -24 + 46x + -16x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -24 + 46x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 23x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 23x + -8x2)' equal to zero and attempt to solve: Simplifying -12 + 23x + -8x2 = 0 Solving -12 + 23x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.5 + -2.875x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2.875x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2.875x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2.875x + x2 = 0 + -1.5 -2.875x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2.875x + x2 = -1.5 The x term is -2.875x. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875x + 2.06640625 + x2 = -1.5 + 2.06640625 Reorder the terms: 2.06640625 + -2.875x + x2 = -1.5 + 2.06640625 Combine like terms: -1.5 + 2.06640625 = 0.56640625 2.06640625 + -2.875x + x2 = 0.56640625 Factor a perfect square on the left side: (x + -1.4375)(x + -1.4375) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (x + -1.4375) equal to 0.752599661 and -0.752599661.Subproblem 1
x + -1.4375 = 0.752599661 Simplifying x + -1.4375 = 0.752599661 Reorder the terms: -1.4375 + x = 0.752599661 Solving -1.4375 + x = 0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + x = 0.752599661 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = 0.752599661 + 1.4375 x = 0.752599661 + 1.4375 Combine like terms: 0.752599661 + 1.4375 = 2.190099661 x = 2.190099661 Simplifying x = 2.190099661Subproblem 2
x + -1.4375 = -0.752599661 Simplifying x + -1.4375 = -0.752599661 Reorder the terms: -1.4375 + x = -0.752599661 Solving -1.4375 + x = -0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + x = -0.752599661 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = -0.752599661 + 1.4375 x = -0.752599661 + 1.4375 Combine like terms: -0.752599661 + 1.4375 = 0.684900339 x = 0.684900339 Simplifying x = 0.684900339Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.190099661, 0.684900339}Solution
x = {2.190099661, 0.684900339}
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