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Simplifying 6x2 + 2x + 2 = 150 Reorder the terms: 2 + 2x + 6x2 = 150 Solving 2 + 2x + 6x2 = 150 Solving for variable 'x'. Reorder the terms: 2 + -150 + 2x + 6x2 = 150 + -150 Combine like terms: 2 + -150 = -148 -148 + 2x + 6x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -148 + 2x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-74 + x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-74 + x + 3x2)' equal to zero and attempt to solve: Simplifying -74 + x + 3x2 = 0 Solving -74 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -24.66666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '24.66666667' to each side of the equation. -24.66666667 + 0.3333333333x + 24.66666667 + x2 = 0 + 24.66666667 Reorder the terms: -24.66666667 + 24.66666667 + 0.3333333333x + x2 = 0 + 24.66666667 Combine like terms: -24.66666667 + 24.66666667 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 24.66666667 0.3333333333x + x2 = 0 + 24.66666667 Combine like terms: 0 + 24.66666667 = 24.66666667 0.3333333333x + x2 = 24.66666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 24.66666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 24.66666667 + 0.25 Combine like terms: 24.66666667 + 0.25 = 24.91666667 0.25 + 0.3333333333x + x2 = 24.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 24.91666667 Calculate the square root of the right side: 4.991659711 Break this problem into two subproblems by setting (x + 0.5) equal to 4.991659711 and -4.991659711.Subproblem 1
x + 0.5 = 4.991659711 Simplifying x + 0.5 = 4.991659711 Reorder the terms: 0.5 + x = 4.991659711 Solving 0.5 + x = 4.991659711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.991659711 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.991659711 + -0.5 x = 4.991659711 + -0.5 Combine like terms: 4.991659711 + -0.5 = 4.491659711 x = 4.491659711 Simplifying x = 4.491659711Subproblem 2
x + 0.5 = -4.991659711 Simplifying x + 0.5 = -4.991659711 Reorder the terms: 0.5 + x = -4.991659711 Solving 0.5 + x = -4.991659711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.991659711 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.991659711 + -0.5 x = -4.991659711 + -0.5 Combine like terms: -4.991659711 + -0.5 = -5.491659711 x = -5.491659711 Simplifying x = -5.491659711Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.491659711, -5.491659711}Solution
x = {4.491659711, -5.491659711}
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