5x+6x*34x-x+18=88

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Solution for 5x+6x*34x-x+18=88 equation:


Simplifying
5x + 6x * 34x + -1x + 18 = 88

Reorder the terms for easier multiplication:
5x + 6 * 34x * x + -1x + 18 = 88

Multiply 6 * 34
5x + 204x * x + -1x + 18 = 88

Multiply x * x
5x + 204x2 + -1x + 18 = 88

Reorder the terms:
18 + 5x + -1x + 204x2 = 88

Combine like terms: 5x + -1x = 4x
18 + 4x + 204x2 = 88

Solving
18 + 4x + 204x2 = 88

Solving for variable 'x'.

Reorder the terms:
18 + -88 + 4x + 204x2 = 88 + -88

Combine like terms: 18 + -88 = -70
-70 + 4x + 204x2 = 88 + -88

Combine like terms: 88 + -88 = 0
-70 + 4x + 204x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 2x + 102x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-35 + 2x + 102x2)' equal to zero and attempt to solve: Simplifying -35 + 2x + 102x2 = 0 Solving -35 + 2x + 102x2 = 0 Begin completing the square. Divide all terms by 102 the coefficient of the squared term: Divide each side by '102'. -0.3431372549 + 0.01960784314x + x2 = 0 Move the constant term to the right: Add '0.3431372549' to each side of the equation. -0.3431372549 + 0.01960784314x + 0.3431372549 + x2 = 0 + 0.3431372549 Reorder the terms: -0.3431372549 + 0.3431372549 + 0.01960784314x + x2 = 0 + 0.3431372549 Combine like terms: -0.3431372549 + 0.3431372549 = 0.0000000000 0.0000000000 + 0.01960784314x + x2 = 0 + 0.3431372549 0.01960784314x + x2 = 0 + 0.3431372549 Combine like terms: 0 + 0.3431372549 = 0.3431372549 0.01960784314x + x2 = 0.3431372549 The x term is 0.01960784314x. Take half its coefficient (0.00980392157). Square it (0.00009611687815) and add it to both sides. Add '0.00009611687815' to each side of the equation. 0.01960784314x + 0.00009611687815 + x2 = 0.3431372549 + 0.00009611687815 Reorder the terms: 0.00009611687815 + 0.01960784314x + x2 = 0.3431372549 + 0.00009611687815 Combine like terms: 0.3431372549 + 0.00009611687815 = 0.34323337177815 0.00009611687815 + 0.01960784314x + x2 = 0.34323337177815 Factor a perfect square on the left side: (x + 0.00980392157)(x + 0.00980392157) = 0.34323337177815 Calculate the square root of the right side: 0.585861222 Break this problem into two subproblems by setting (x + 0.00980392157) equal to 0.585861222 and -0.585861222.

Subproblem 1

x + 0.00980392157 = 0.585861222 Simplifying x + 0.00980392157 = 0.585861222 Reorder the terms: 0.00980392157 + x = 0.585861222 Solving 0.00980392157 + x = 0.585861222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00980392157' to each side of the equation. 0.00980392157 + -0.00980392157 + x = 0.585861222 + -0.00980392157 Combine like terms: 0.00980392157 + -0.00980392157 = 0.00000000000 0.00000000000 + x = 0.585861222 + -0.00980392157 x = 0.585861222 + -0.00980392157 Combine like terms: 0.585861222 + -0.00980392157 = 0.57605730043 x = 0.57605730043 Simplifying x = 0.57605730043

Subproblem 2

x + 0.00980392157 = -0.585861222 Simplifying x + 0.00980392157 = -0.585861222 Reorder the terms: 0.00980392157 + x = -0.585861222 Solving 0.00980392157 + x = -0.585861222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00980392157' to each side of the equation. 0.00980392157 + -0.00980392157 + x = -0.585861222 + -0.00980392157 Combine like terms: 0.00980392157 + -0.00980392157 = 0.00000000000 0.00000000000 + x = -0.585861222 + -0.00980392157 x = -0.585861222 + -0.00980392157 Combine like terms: -0.585861222 + -0.00980392157 = -0.59566514357 x = -0.59566514357 Simplifying x = -0.59566514357

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.57605730043, -0.59566514357}

Solution

x = {0.57605730043, -0.59566514357}

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