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Simplifying 2x2 + 28x = 1156 Reorder the terms: 28x + 2x2 = 1156 Solving 28x + 2x2 = 1156 Solving for variable 'x'. Reorder the terms: -1156 + 28x + 2x2 = 1156 + -1156 Combine like terms: 1156 + -1156 = 0 -1156 + 28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-578 + 14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-578 + 14x + x2)' equal to zero and attempt to solve: Simplifying -578 + 14x + x2 = 0 Solving -578 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '578' to each side of the equation. -578 + 14x + 578 + x2 = 0 + 578 Reorder the terms: -578 + 578 + 14x + x2 = 0 + 578 Combine like terms: -578 + 578 = 0 0 + 14x + x2 = 0 + 578 14x + x2 = 0 + 578 Combine like terms: 0 + 578 = 578 14x + x2 = 578 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 578 + 49 Reorder the terms: 49 + 14x + x2 = 578 + 49 Combine like terms: 578 + 49 = 627 49 + 14x + x2 = 627 Factor a perfect square on the left side: (x + 7)(x + 7) = 627 Calculate the square root of the right side: 25.039968051 Break this problem into two subproblems by setting (x + 7) equal to 25.039968051 and -25.039968051.Subproblem 1
x + 7 = 25.039968051 Simplifying x + 7 = 25.039968051 Reorder the terms: 7 + x = 25.039968051 Solving 7 + x = 25.039968051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 25.039968051 + -7 Combine like terms: 7 + -7 = 0 0 + x = 25.039968051 + -7 x = 25.039968051 + -7 Combine like terms: 25.039968051 + -7 = 18.039968051 x = 18.039968051 Simplifying x = 18.039968051Subproblem 2
x + 7 = -25.039968051 Simplifying x + 7 = -25.039968051 Reorder the terms: 7 + x = -25.039968051 Solving 7 + x = -25.039968051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -25.039968051 + -7 Combine like terms: 7 + -7 = 0 0 + x = -25.039968051 + -7 x = -25.039968051 + -7 Combine like terms: -25.039968051 + -7 = -32.039968051 x = -32.039968051 Simplifying x = -32.039968051Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.039968051, -32.039968051}Solution
x = {18.039968051, -32.039968051}
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