4(x^2-28x+98)=0

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Solution for 4(x^2-28x+98)=0 equation:


Simplifying
4(x2 + -28x + 98) = 0

Reorder the terms:
4(98 + -28x + x2) = 0
(98 * 4 + -28x * 4 + x2 * 4) = 0
(392 + -112x + 4x2) = 0

Solving
392 + -112x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(98 + -28x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(98 + -28x + x2)' equal to zero and attempt to solve: Simplifying 98 + -28x + x2 = 0 Solving 98 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + -28x + -98 + x2 = 0 + -98 Reorder the terms: 98 + -98 + -28x + x2 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + -28x + x2 = 0 + -98 -28x + x2 = 0 + -98 Combine like terms: 0 + -98 = -98 -28x + x2 = -98 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -98 + 196 Reorder the terms: 196 + -28x + x2 = -98 + 196 Combine like terms: -98 + 196 = 98 196 + -28x + x2 = 98 Factor a perfect square on the left side: (x + -14)(x + -14) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -14) equal to 9.899494937 and -9.899494937.

Subproblem 1

x + -14 = 9.899494937 Simplifying x + -14 = 9.899494937 Reorder the terms: -14 + x = 9.899494937 Solving -14 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 9.899494937 + 14 Combine like terms: -14 + 14 = 0 0 + x = 9.899494937 + 14 x = 9.899494937 + 14 Combine like terms: 9.899494937 + 14 = 23.899494937 x = 23.899494937 Simplifying x = 23.899494937

Subproblem 2

x + -14 = -9.899494937 Simplifying x + -14 = -9.899494937 Reorder the terms: -14 + x = -9.899494937 Solving -14 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -9.899494937 + 14 Combine like terms: -14 + 14 = 0 0 + x = -9.899494937 + 14 x = -9.899494937 + 14 Combine like terms: -9.899494937 + 14 = 4.100505063 x = 4.100505063 Simplifying x = 4.100505063

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.899494937, 4.100505063}

Solution

x = {23.899494937, 4.100505063}

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